Learn – Calculus – Indefinite Integrals

1 Indefinite integral
- 1.1 Exercises

Indefinite integral

Exercises

Problem set

For the function $x^2$ , give an expression for accumulation function $\mbox{AF}_1(x)$ as an integral.
For the function $\frac{1}{x}$ , give an expression for accumulation function $\mbox{AF}_{-2}(x)$ as an integral.
For the function $\sin x^2$ , give an expression for accumulation function $\mbox{AF}_{\pi}(x)$ as an integral.
For the function $e^{x^2}$ , give an expression for the value $\mbox{AF}_{2}(9)$ as an integral.
For the function $\frac{1}{\ln x}$ , give an expression for the value $\mbox{AF}_{4}(6)$ as an integral.

Problem set

Evaluate the following.

$\int \sin x\, dx$
$\int 2^x\, dx$
$\int \frac{1}{x} + \frac{1}{x^2}\, dx$
$\int \frac{3}{x} - \frac{5}{x^3}\, dx$

Problem set

Evaluate the following.

$\int e^{\tan x}\sec^2 x\, dx$
$\int \sin^3 x \cos x\, dx$
$\int 2^{\cos x}\sin x\, dx$
$\int \frac{1}{x\ln x}\, dx$
$\int e^{e^x}e^x\, dx$

Problem set

Evaluate the following.

$\int e^{5x}\, dx$
$\int \sin 2x\, dx$
$\int \sqrt{3x+3}\, dx$
$\int \left(\frac{x}{2} + 1.3\right)^{100}\, dx$
$\int e^{2x} + (3x+1)^3 + \sin 10x\, dx$

Problem set

Evaluate the following.

$\int \frac{x}{x^2+5}\, dx$
$\int x^2\sec^2(5-x^3)\, dx$
$\int \frac{x^{99}}{99x^{100}+51}\, dx$
$\int \frac{x-2x^3}{x^2-x^4}\, dx$
$\int \frac{\ln x}{x}\, dx$

Problem set

Evaluate the following.

$\int \csc^2 x\cot x\, dx$
$\int \sec^3 x\tan x\, dx$
$\int \csc^3 x\cot x\, dx$
$\int \csc^2 x\cot^7 x\, dx$
$\int \tan x\, dx$
$\int \cot x\, dx$
$\int \sec x\, dx$
$\int \csc x\, dx$

Problem set

Evaluate the following.

$\int \tan (2x+3)\, dx$
$\int e^x\sec e^x\tan e^x\, dx$
$\int \sec^5 (-10x-5)\tan (-10x-5)\, dx$
$\int xe^{3x^2}\, dx$

Problem set

Evaluate the following.

$\int \sec^4 x\, dx$

Problem set

Evaluate the following.

$\int xe^x\, dx$
$\int x2^x\, dx$
$\int x\sin x\, dx$
$\int x\sqrt{x-3}\, dx$
$\int x\sin 2x+3\, dx$
$\int x\sec^2 x\, dx$
$\int x\csc^2{\frac{x}{2}}\, dx$

Problem set

Evaluate the following.

$\int x^2e^x\, dx$
$\int x^3\sin x\, dx$
$\int x^4\cos x\, dx$
$\int x^3\sqrt{x-3}\, dx$
$\int x^2\sqrt{3-2x}\, dx$

Problem set

Evaluate the following.

$\int x\ln x\, dx$
$\int \ln x\, dx$
$\int x^3\ln x\, dx$
$\int (\ln x)^2\, dx$
$\int x\cot^2 x\, dx$
$\int x\tan^2 x\, dx$

Problem set

Evaluate the following.

$\int e^x\sin x\, dx$
$\int 2^x\cos x\, dx$

Problem set

Evaluate the following.

$\int \arcsin x\, dx$
$\int \arctan x\, dx$