Learn Integrals with Examples and Practice Problems

How to compute
$\int \frac{\sin x}{2 \cos 2 x} d x$

Eileen Garza 2022-04-20

How to calculate:
$\int_{0}^{2 π} \sqrt{1 - \sin^{2} θ} d θ$

Reagan Gomez 2022-04-16

How do I solve the following?
$lim_{x \to 0} \int_{0}^{1} \cos (\frac{1}{x t}) d t$

Haylee Bowen 2022-04-15

How do I solve this:
$\int_{0}^{1} \frac{\log (x^{2} - 2 x \cos a + 1)}{x} d x$

Raven Gardner 2022-04-13

How do I prove the correctness of the following formula relating to the fundamental theorem of calculus?
$\int x \cos 3 x d x = \frac{\cos 3 x}{9} + \frac{x \sin 3 x}{3} + C$

Deacon Simpson 2022-04-12

How do I prove that $\int e^{x t} d t = \frac{e^{x t}}{x} + C$

velinariojepvg 2022-04-12

How to take limits of 'almost Riemann' sums like $lim_{n \to \infty} \sum_{k = 0}^{n} \frac{1}{n} \cos (a π k \log (n) / n)$

Matthew Hubbard 2022-04-10

Solving $\int_{0}^{2} z^{n - a - 2} (2 - z^{- 1})^{b} d z$ by using beta function

Deja Vaughn 2022-04-09

Trying to solve this tricky one:
$\int e^{2 x} \sqrt{1 + e^{2 x}} d x$

Christopher Stone 2022-04-09

There's an integral I've no idea how to solve. Even Wolfram|Alpha gives a very odd result.
$\int \frac{\sqrt{1 - x^{2}} + \sqrt{1 + x^{2}}}{\sqrt{1 - x^{4}}} d x$

zdebe5l8 2022-04-09

The question is, find the integral to the function:
$\frac{\sin^{3} θ}{\sin^{3} θ - \cos^{3} θ}$

Alessandra Carrillo 2022-04-08

I'm trying to solve
$\int_{- \infty}^{\infty} \frac{1}{(4 + x^{2}) \sqrt{4 + x^{2}}} d x$

Jasiah Vincent 2022-04-08

I would like to integrate:
$\int \frac{d t}{e^{2 t} (e^{t} + 1)}$

Leonard Montes 2022-04-08

I want to find a nice simple expression for the definite integral
$\int_{0}^{\infty} \frac{x^{2} d x}{{(x^{2} - a^{2})}^{2} + x^{2}}$

Aldo Fernandez 2022-04-08

I ran across this integration problem that has an interesting pattern.
$\int_{0}^{(n - 1) π} \frac{1}{\tan^{n} (x) + 1} d x = \frac{(n - 1) π}{2}$

Justine White 2022-04-08

I need to evaluate
$\int_{0}^{1} \frac{\log (x)}{1 - x} d x$

Ormezzani6cuu 2022-04-07

How to integrate
$\int \frac{3 x^{2} + x + 4}{x^{3} + x} d x$

Jasiah Vincent 2022-04-06

How to integrate:
$\int_{\sqrt{\ln 2}}^{\sqrt{\ln 3}} \frac{x \cdot \sin (x^{2})}{\sin (x^{2}) + \sin (\ln 6 - x^{2})} d x$

Yaritza Estrada 2022-04-05

Find:
$lim_{t \to \infty} [e^{- t} \int_{0}^{t} \int_{0}^{t} \frac{e^{x} - e^{y}}{x - y} d x d y]$

Adolfo Hebert 2022-04-05

Evaluating the integral,
$\int_{0}^{\infty} \ln (1 - e^{- x}) d x$

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Calculus 1

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