# Tagged Questions

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### Integration of $x^3 e^x$

I am beginner in calculus and I am struggling with this integral: $$\int x^{3}e^{x}\mathrm{d}x$$ If anyone could give me some hints, any help will be appreciated.
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### Integration with exponential

$$\int y\,e^{x^2}\,dy$$ I begin with $$\int e^{x^2}y\, dy$$ let $u=e^x$, $du=e^x\, dx$ how do I continue?
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### Simplifying expression and finding indefinite integral

(a) Simplify $$\Large \frac{e^{-4x} + 3e^{-2x}}{e^{-4x}-9} \quad.$$ (b) Hence find $$\Large \int\frac{e^{-4x} + 3e^{-2x}}{e^{-4x}-9} \mathrm{d}x$$ I tried to find a breakdown of the expression, but ...
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### Solving integral that contain exponential function and lower incomplete gamma function

I have the following integral; $$y=\int_0^\infty\frac{e^{-xf}}{m+x}\gamma(a,hx)~dx$$ where $f,m,h\in\mathbb{R}^+$ , $a\in\mathbb{N}$ , $\gamma\left(a,h x\right)$ is the lower incomplete gamma ...
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### Normalizing a probability density function

I need to find a normalization term $N(\alpha,\beta)$ for the probability density function: $$PDF(\alpha,\beta)=(x-x_1)^{\alpha}e^{-\beta(x-x_1)}$$ In other words, solve the following equation: ...
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### Contour integral $\int^\pi_{-\pi}(a-\cos\theta)^b\exp(c\cos\theta)d\theta$ assuming $a>1$, $b>0$, $c>0$

Under the condition $a>1$, $b>0$, $c>0$, is there any good function to express the following integral? $$\int^\pi_{-\pi}\left(a-\cos\theta\right)^b\exp\left(c\cos\theta\right)d\theta$$ I ...
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### What is the integral containing decaying exponential function?

I am trying to figure out properties of the following integral: $$p(t)=\int_{0}^{t} e^{\alpha(t-t')} f(t')dt', \hspace{1 cm} t>t'$$ I would google and read more info about this integral but I do ...
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### Integration of $g(x) = e^{f(x)}$ [closed]

Is there any way of simplifying this integral? $$f(x) = \int e^{2x^3}\,dx$$
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### How to evaluate the integral $\int_0^{\ln3} e^{x-e^x}\,\mathrm dx$?

How to evaluate the following definite integral? $$\int_0^{\ln3} e^{x-e^x}\,\mathrm dx.$$ Should I use some sort of U Substitution?
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### Integral involving Modified Bessel function, exponential and power

I am trying to evaluate the following integral: $$\int_{b y}^\infty \frac{e^{-x}(-1+I_0[2\sqrt{bx}]-\sqrt{bx}I_1[2\sqrt{bx}])}{x^2}dx$$ Even though there are a lot of integrals involving the ...
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### Calculate $10,000e^{-\int_2^{10}\left(0.05+0.01/(t+1)\right)\,dt}$

This equation is used as an example in a text book with a given answer of $\approx$ 6,617 I cannot get to this solution as somewhere along the way I must be making an error. If it is a problem with ...