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.

Set of formulas for indefinite integrals of elementary functions.

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

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

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

Indefinite integral - example 3
Solved example with indefinite integral of function f(x)=(1+sinx)^{1/2}·cosx.

Solved example with indefinite integral of function f(x)=x·e^{x}. Theorem about integration by parts is used.

Solved example with indefinite integral of function f(x)=x^{3}·ln(x). Theorem about integration by parts is used.

Solved example with indefinite integral of function f(x)=x^{2}·e^{x}. 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.

Solved example with indefinite integral of function f(x)=x^{3}·e^{x2}. 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.

Solved example with indefinite integral of function f(x)=3^{5·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.

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
Solved example with indefinite integral of function f(x)=2/(cos^{2}(3·x)). In example theorem about integration by substitution is applied.

Solved example with indefinite integral of function f(x)=1/(1-sin^{2}(x)). Pythagorean identity is applied during calculations. Application of Pythagorean identity allows to recalculate function to form of elementary function.

Solved example with indefinite integral of function f(x)=(1-sin^{2}(x))/cos(x). Pythagorean identity is applied during calculations. Application of Pythagorean identity allows to recalculate function to form of elementary function. Pythagorean identity → sin^{2}x + cos^{2}x = 1.

Solved example with indefinite integral of function f(x)=(1-cos^{2}(x))/sin(x). Pythagorean identity is applied during calculations. Application of Pythagorean identity allows to recalculate function to form of elementary function. Pythagorean identity → sin^{2}x + cos^{2}x = 1.

Solved example with indefinite integral of function f(x)=1/(x^{2}+8). In example theorem about integration by substitution is applied. Formulas for integrals of elementary functions are also used.