# Tagged Questions

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### Integral of the exponential function

I am searching the indefinite integral of this function: $\dfrac{\exp(x)}{(1+x)^{5/3}}$. Thank you alot.
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### Integral of an exponential of rational function

I have an integral of the form $\int_{a}^{b} \text{exp}\left(\frac{\lambda}{\rho^2 m + \sigma^2_u}\right) \frac{1}{m^2}\text{exp}\left(-\frac{\lambda}{m}\right)$. Can this be found analytically?
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### Definite integration of a exponential function mixed with rational functions

Suppose $a>0$ , I am interested in a solution of the following definite integral: $$\int_{1}^{\infty}\frac{\exp({-az})}{z \sqrt{z^2-1}}{\,dz}$$ Thank you.
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### Calculation of integral $\int\exp \left(-\alpha \sin^2 \left(\frac{x}{2} \right) \right) dx$

Given $\alpha$ is a constant. How to calculate the following integral? $$\int \exp \bigg(-\alpha \sin^2 \bigg(\frac{x}{2} \bigg) \bigg) dx$$ Thanks for your answer.
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### Double integrals of exponential functions

I need to find the double integral of $$e^{\frac{x}{y^2}}$$ bound by the $y\mbox{-axis}$, $x=y^2$, $y=1$, and $y=2$. The limits of integration were easy to find, but I am pretty confused about how to ...
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### Integral of exponential using error function

I'm trying to solve some integrals below $$\int_{-\infty}^{\infty} {x^n e^\frac{-(x - \mu)^2}{\sigma^2}}dx$$ I am interested in the solutions where n = 0, 1, 2, 3, 4. I have learned that ...
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### Integrating exponential of exponential function: stuck at integration by parts

I want to integrate $$\int_{0}^{t}\exp\left\{{k_{1}\left ( 1-e^{-t/{k_{2}}} \right )}\right\}dt$$ First I substituted $u = 1-e^{-t/{k_{2}}}$ Thus I get ...
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### how to double integrate this exponential function

how can i integrate this $\int_0^∞\int_x^∞{\frac{e^{-y}}{y}}dy dx$ i am stuck here $\int{\frac{e^{-y}}{y}}dy$. I have tried some log substitutions.
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### Integral of exponential with second degree exponent

I want to compute the integral $$\int_\mathbb{R}e^{-t\left(y-\dfrac{(at+x)i}{2t}\right)^2}dy$$ I know that $\int_\mathbb{R}e^{-ty^2}dy=\sqrt{\pi/t}$, but here there is an extra imaginary factor. What ...
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### A closed form for $\int_0^\infty\left(\frac{2^{-x}-3^{-x}}x\right)^adx,\ a\notin\mathbb{Z}^+$

Let $$I(a)=\int_0^\infty\left(\frac{2^{-x}-3^{-x}}x\right)^adx.$$ $I(a)$ has closed form representations for all $a\in\mathbb{Z}^+$. Is there any algebraic (or at least period) ...
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### Need help with $\int_0^2\frac{1}{2+\sqrt{3\,e^x+3\,e^{-x}-2}}dx$

Could you please help me to solve this integration problem? $$\int_0^2\frac{1}{2+\sqrt{3\,e^x+3\,e^{-x}-2}}dx$$ Its approximate numeric value is $0.419197813818367...$, but I could not find an exact ...
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### Integrate Exponential function with Integration Variable e (de)

I have the following problem: How do i integrate this: $\int^1_0 e^{x^2+3 } de$ ? Whats putting me off is the de, i don't know how to integrate over the e-function... According to Wolfram Alpha, ...
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### Gamma Type Integral

I was hoping someone could help me with a question I came across recently: essentially it's a gamma type integral that your asked to evaluate/reduce: ...
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### How to put exp function back in the integral?

Thanks to everybody in advance. I have this integral: $$e^{-at} \int_{0}^{t} e^{au}f(u) du$$ where f(t) is something I can't integrate. Is there a way to put the exponential function back in the ...
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### Can anyone help with solving this integral?

I would like to solve this indefinite integral. I was practicing figuring out integrals when this one stumped me. WolframAlpha seems to have calculated it using some numerical method. I feel like this ...
Does anybody know how to solve the following singular integral: $$\int_0^\pi \frac{\text{e}^{-i\cdot a\cdot \cos(x)}}{\cos(x)-b}\,\text{d}x$$ with $x$, $a$ and $b$ being real-valued. Do integrals ...
I need to integrate $0.095x^{-0.26}[1-(1+\frac{a}{x})^{-0.2}]$. However, I am not sure how to multiply the exponents and then integrate it. Am I missing something easy?