Learn Integrals with Examples and Practice Problems

$\int_{- \infty}^{\infty} e^{- \frac{1}{2} x^{2}} d x$ and $\int_{- \infty}^{\infty} x^{2} e^{- \frac{1}{2} x^{2}} d x$
how i compute these integrals via Gauss Integral?

Tara Alvarado 2022-01-03

Proof that:
$\int_{0}^{\frac{π}{2}} \ln (1 + α \sin^{2} x) d x = π \ln \frac{1 + \sqrt{1 + α}}{2}$

Concepcion Hale 2022-01-03

Evaluate integral:
$\int_{0}^{\frac{π}{3}} \ln^{2} (\frac{\sin x}{\sin (x + \frac{π}{3})}) d x$

Ernest Ryland 2022-01-03

How to integrate
$\frac{\cos (7 x) - \cos (8 x)}{1 + 2 \cos (5 x)}$

Francisca Rodden 2022-01-03

Show that:
$\int_{0}^{\infty} \frac{\sin^{3} (x)}{x^{3}} d x = \frac{3 π}{8}$

Lennie Davis 2022-01-03

How can I prove that?
$\int_{0}^{1} \frac{\ln (x)}{x^{2} - 1} d x = \frac{π^{2}}{8}$

sunshine022uv 2022-01-03

Find out
$\int e^{\cos x} d x$

Oberlaudacu 2022-01-03

How can I evaluate
$\int_{- \infty}^{\infty} \frac{\cos x}{cosh x} d x$ and $\int_{0}^{\infty} \frac{\sin x}{e^{x} - 1} d x$

Kelly Nelson 2022-01-03

Solve the integral:
$\int \frac{1}{x^{2 n} + 1} d x$

piarepm 2022-01-03

Finding integral:
$\int_{0}^{1} \frac{\ln (1 + x)}{x} d x$

Julia White 2022-01-03

How to calculate
$\int \frac{x^{2}}{{(x^{2} + 1)}^{2}} d x$

Concepcion Hale 2022-01-03

Evaluate integral :
$\int \cos^{4} (x) d x$

tearstreakdl 2022-01-03

How to do the following integral:
$\int_{0}^{1} \frac{x^{a} - 1}{\log (x)} d x$
where $a \geq 0$ ?

Arthur Pratt 2022-01-03

Show that
$\int_{0}^{\infty} \frac{x \cos a x}{sinh x} d x \frac{π^{2}}{4} {sech}^{2} (\frac{a π}{2})$

Francisca Rodden 2022-01-03

Compute
$\int_{0}^{1} \frac{\ln (x + 1)}{x^{2} + 1} d x$

Salvatore Boone 2022-01-03

What are the usual ways to follow in order to solve the integrals given below?
$I = \int_{0}^{1} \ln Γ (x) d x$
$J = \int_{0}^{1} x Γ (x) d x$

elvishwitchxyp 2022-01-03

Why is the integral of $d \sqrt{1 + x^{2}}$ simply equal to $\sqrt{1 + x^{2}}$ ?

veksetz 2022-01-02

Double Integrals involving infinity
$\int_{0}^{\infty} \int_{0}^{\infty} x y e^{- (x^{2} + y^{2})} d x d y$

Charles Kingsley 2022-01-02

How can I find the principal value of the following?
$P V \int_{- \infty}^{\infty} \frac{e^{i x}}{x (x^{2} + x + 1)} d x$

kloseyq 2022-01-02

The question is: using the comparison test for improper integrals state if
$\int_{0}^{\infty} x^{4} e^{- x} d x$ converges or not.

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Calculus 1

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