 # Indefinite integrals examples

Collection of examples with solutions indefinite integrals. Functions integration is inverse operation in comparison to functions derivatives calculation. In general integration is a summing of elementary elements dx.

## Indefinite integrals of elementary functions Set of formulas for indefinite integrals of elementary functions.

Indefinite integrals of elementary functions

## Indefinite integral example 1 Solved example with indefinite integral of function f(x)=sin(4·x)/(1+2·cos(4·x)).

Indefinite integral - example 1

## Indefinite integral example 2 Solved example with indefinite integral of function f(x)=(3·x+7)1/2.

Indefinite integral - example 2

## Indefinite integral example 3 Solved example with indefinite integral of function f(x)=2/(3·x+1).

Indefinite integral - example 3

## Indefinite integral example 4 Solved example with indefinite integral of function f(x)=(1+sinx)1/2·cosx.

Indefinite integral - example 4

## Indefinite integral example 5 Solved example with indefinite integral of function f(x)=x·ex. Theorem about integration by parts is used.

Indefinite integral - example 5

## Indefinite integral example 6 Solved example with indefinite integral of function f(x)=x3·ln(x). Theorem about integration by parts is used.

Indefinite integral - example 6

## Indefinite integral example 7 Solved example with indefinite integral of function f(x)=x2·ex. In example theorem about integration by parts is used twice. At the end of integration, a derivative of integrated function is calculated in purpose to check integration correctness.

Indefinite integral - example 7

## Indefinite integral example 8 Solved example with indefinite integral of function f(x)=x3·ex2. In example theorem about integration by parts is used three times. At the end of integration, a derivative of integrated function is calculated in purpose to check integration correctness.

Indefinite integral - example 8

## Indefinite integral example 9 Solved example with indefinite integral of function f(x)=35·x. In example theorem about integration by substitution is applied. At the end of integration, a derivative of integrated function is calculated in purpose to check integration correctness.

Indefinite integral - example 9

## Indefinite integral example 10 Solved example with indefinite integral of function f(x)=sin(x/2)+cos(2·x). In example theorem about integration a sum of two functions is applied.

Indefinite integral - example 10

## Indefinite integral example 11 Solved example with indefinite integral of function f(x)=2/(cos2(3·x)). In example theorem about integration by substitution is applied.

Indefinite integral - example 11

## Indefinite integral example 12 Solved example with indefinite integral of function f(x)=1/(1-sin2(x)). Pythagorean identity is applied during calculations. Application of Pythagorean identity allows to recalculate function to form of elementary function.

Indefinite integral - example 12

## Indefinite integral example 13 Solved example with indefinite integral of function f(x)=(1-sin2(x))/cos(x). Pythagorean identity is applied during calculations. Application of Pythagorean identity allows to recalculate function to form of elementary function. Pythagorean identity → sin2x + cos2x = 1.

Indefinite integral - example 13

## Indefinite integral example 14 Solved example with indefinite integral of function f(x)=(1-cos2(x))/sin(x). Pythagorean identity is applied during calculations. Application of Pythagorean identity allows to recalculate function to form of elementary function. Pythagorean identity → sin2x + cos2x = 1.

Indefinite integral - example 14

## Indefinite integral example 15 Solved example with indefinite integral of function f(x)=1/(x2+8). In example theorem about integration by substitution is applied. Formulas for integrals of elementary functions are also used.

Indefinite integral - example 15