Integral $cosleft(lnleft(e^t+1right)+at+bright)dt$
I am trying to solve this integral:
$$int cosleft(lnleft(e^t+1right)+at+bright)dt
$$ with $$a, b in Re$$
I can solve this:
$$int cosleft(lnleft(xright)right)dt
$$
Defining: $u=cos(ln(x))$ and $v = frac{1}{x}$. Then using the fomular two times:
$$int udv=uv-int vdu$$
I can get the solution
$$frac {1}{2}xcos(ln(x))+ frac {1}{2}xsin(ln(x)) +C$$
I also found the orther topic in our website The integral $intln(x)cos(1+(ln(x))^2),dx$. But still have no idea with this.
I wonder is this non-integrable function ?!
integration trigonometric-integrals
edited Dec 9 at 7:17
user1101010
7571630
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
add a comment |
I am trying to solve this integral:
$$int cosleft(lnleft(e^t+1right)+at+bright)dt
$$ with $$a, b in Re$$
I can solve this:
$$int cosleft(lnleft(xright)right)dt
$$
Defining: $u=cos(ln(x))$ and $v = frac{1}{x}$. Then using the fomular two times:
$$int udv=uv-int vdu$$
I can get the solution
$$frac {1}{2}xcos(ln(x))+ frac {1}{2}xsin(ln(x)) +C$$
I also found the orther topic in our website The integral $intln(x)cos(1+(ln(x))^2),dx$. But still have no idea with this.
I wonder is this non-integrable function ?!
integration trigonometric-integrals
edited Dec 9 at 7:17
user1101010
7571630
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
Where this problem arise? For particular values of $a,b,t$ the integrand function is not even defined. Anyway any continuous function is integrable over closed intervals of $mathbb{R}$, but I won't bet a penny on the fact that $(e^t+at+b)^i$ has a primitive which can be expressed in terms of elementary functions.
– Jack D'Aurizio
Dec 9 at 6:40
I typed wrong equation. But i don't know how to rewrite my question. My question is about this: $int cosleft(lnleft(e^t+1right)+at+bright)dt$
– Thiều Quang Minh Nhật
Dec 9 at 6:41
I derived this integration from the dynamic and kinematic equation of autonomous underwater vehicle (AUV) when I consider a turning motion of AUV. This is X coordinate.
– Thiều Quang Minh Nhật
Dec 9 at 6:45
2
I tried both wxmaxima and sympy. Both cannot integrate it symbolically (of course, its antiderivative still exists since it is continuous).
– Alex Vong
Dec 9 at 8:44
Does anyone have an idea?
– Thiều Quang Minh Nhật
Dec 13 at 7:02
add a comment |
I am trying to solve this integral:
$$int cosleft(lnleft(e^t+1right)+at+bright)dt
$$ with $$a, b in Re$$
I can solve this:
$$int cosleft(lnleft(xright)right)dt
$$
Defining: $u=cos(ln(x))$ and $v = frac{1}{x}$. Then using the fomular two times:
$$int udv=uv-int vdu$$
I can get the solution
$$frac {1}{2}xcos(ln(x))+ frac {1}{2}xsin(ln(x)) +C$$
I also found the orther topic in our website The integral $intln(x)cos(1+(ln(x))^2),dx$. But still have no idea with this.
I wonder is this non-integrable function ?!
integration trigonometric-integrals
edited Dec 9 at 7:17
user1101010
7571630
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
I am trying to solve this integral:
$$int cosleft(lnleft(e^t+1right)+at+bright)dt
$$ with $$a, b in Re$$
I can solve this:
$$int cosleft(lnleft(xright)right)dt
$$
Defining: $u=cos(ln(x))$ and $v = frac{1}{x}$. Then using the fomular two times:
$$int udv=uv-int vdu$$
I can get the solution
$$frac {1}{2}xcos(ln(x))+ frac {1}{2}xsin(ln(x)) +C$$
I also found the orther topic in our website The integral $intln(x)cos(1+(ln(x))^2),dx$. But still have no idea with this.
I wonder is this non-integrable function ?!
integration trigonometric-integrals
integration trigonometric-integrals
edited Dec 9 at 7:17
user1101010
7571630
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
edited Dec 9 at 7:17
user1101010
7571630
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
edited Dec 9 at 7:17
user1101010
7571630
edited Dec 9 at 7:17
user1101010
7571630
edited Dec 9 at 7:17
user1101010
7571630
7571630
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
asked Dec 9 at 6:35
Thiều Quang Minh Nhật
314
314
Where this problem arise? For particular values of $a,b,t$ the integrand function is not even defined. Anyway any continuous function is integrable over closed intervals of $mathbb{R}$, but I won't bet a penny on the fact that $(e^t+at+b)^i$ has a primitive which can be expressed in terms of elementary functions.
– Jack D'Aurizio
Dec 9 at 6:40
I typed wrong equation. But i don't know how to rewrite my question. My question is about this: $int cosleft(lnleft(e^t+1right)+at+bright)dt$
– Thiều Quang Minh Nhật
Dec 9 at 6:41
I derived this integration from the dynamic and kinematic equation of autonomous underwater vehicle (AUV) when I consider a turning motion of AUV. This is X coordinate.
– Thiều Quang Minh Nhật
Dec 9 at 6:45
2
I tried both wxmaxima and sympy. Both cannot integrate it symbolically (of course, its antiderivative still exists since it is continuous).
– Alex Vong
Dec 9 at 8:44
Does anyone have an idea?
– Thiều Quang Minh Nhật
Dec 13 at 7:02
add a comment |
Where this problem arise? For particular values of $a,b,t$ the integrand function is not even defined. Anyway any continuous function is integrable over closed intervals of $mathbb{R}$, but I won't bet a penny on the fact that $(e^t+at+b)^i$ has a primitive which can be expressed in terms of elementary functions.
– Jack D'Aurizio
Dec 9 at 6:40
I typed wrong equation. But i don't know how to rewrite my question. My question is about this: $int cosleft(lnleft(e^t+1right)+at+bright)dt$
– Thiều Quang Minh Nhật
Dec 9 at 6:41
I derived this integration from the dynamic and kinematic equation of autonomous underwater vehicle (AUV) when I consider a turning motion of AUV. This is X coordinate.
– Thiều Quang Minh Nhật
Dec 9 at 6:45
2
I tried both wxmaxima and sympy. Both cannot integrate it symbolically (of course, its antiderivative still exists since it is continuous).
– Alex Vong
Dec 9 at 8:44
Does anyone have an idea?
– Thiều Quang Minh Nhật
Dec 13 at 7:02
Where this problem arise? For particular values of $a,b,t$ the integrand function is not even defined. Anyway any continuous function is integrable over closed intervals of $mathbb{R}$, but I won't bet a penny on the fact that $(e^t+at+b)^i$ has a primitive which can be expressed in terms of elementary functions.
– Jack D'Aurizio
Dec 9 at 6:40
Where this problem arise? For particular values of $a,b,t$ the integrand function is not even defined. Anyway any continuous function is integrable over closed intervals of $mathbb{R}$, but I won't bet a penny on the fact that $(e^t+at+b)^i$ has a primitive which can be expressed in terms of elementary functions.
– Jack D'Aurizio
Dec 9 at 6:40
I typed wrong equation. But i don't know how to rewrite my question. My question is about this: $int cosleft(lnleft(e^t+1right)+at+bright)dt$
– Thiều Quang Minh Nhật
Dec 9 at 6:41
I typed wrong equation. But i don't know how to rewrite my question. My question is about this: $int cosleft(lnleft(e^t+1right)+at+bright)dt$
– Thiều Quang Minh Nhật
Dec 9 at 6:41
I derived this integration from the dynamic and kinematic equation of autonomous underwater vehicle (AUV) when I consider a turning motion of AUV. This is X coordinate.
– Thiều Quang Minh Nhật
Dec 9 at 6:45
I derived this integration from the dynamic and kinematic equation of autonomous underwater vehicle (AUV) when I consider a turning motion of AUV. This is X coordinate.
– Thiều Quang Minh Nhật
Dec 9 at 6:45
2
2
I tried both wxmaxima and sympy. Both cannot integrate it symbolically (of course, its antiderivative still exists since it is continuous).
– Alex Vong
Dec 9 at 8:44
I tried both wxmaxima and sympy. Both cannot integrate it symbolically (of course, its antiderivative still exists since it is continuous).
– Alex Vong
Dec 9 at 8:44
Does anyone have an idea?
– Thiều Quang Minh Nhật
Dec 13 at 7:02
Does anyone have an idea?
– Thiều Quang Minh Nhật
Dec 13 at 7:02
add a comment |
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Where this problem arise? For particular values of $a,b,t$ the integrand function is not even defined. Anyway any continuous function is integrable over closed intervals of $mathbb{R}$, but I won't bet a penny on the fact that $(e^t+at+b)^i$ has a primitive which can be expressed in terms of elementary functions.
– Jack D'Aurizio
Dec 9 at 6:40
I typed wrong equation. But i don't know how to rewrite my question. My question is about this: $int cosleft(lnleft(e^t+1right)+at+bright)dt$
– Thiều Quang Minh Nhật
Dec 9 at 6:41
I derived this integration from the dynamic and kinematic equation of autonomous underwater vehicle (AUV) when I consider a turning motion of AUV. This is X coordinate.
– Thiều Quang Minh Nhật
Dec 9 at 6:45
2
I tried both wxmaxima and sympy. Both cannot integrate it symbolically (of course, its antiderivative still exists since it is continuous).
– Alex Vong
Dec 9 at 8:44
Does anyone have an idea?
– Thiều Quang Minh Nhật
Dec 13 at 7:02