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# Integrals of Polynomial Functions Calculator

## Get detailed solutions to your math problems with our Integrals of Polynomial Functions step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Solved example of integrals of polynomial functions

$\int\left(x^2+2x+1\right)dx$
2

Expand the integral $\int\left(x^2+2x+1\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately

$\int x^2dx+\int2xdx+\int1dx$

Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, such as $2$

$\frac{x^{3}}{3}$
3

The integral $\int x^2dx$ results in: $\frac{x^{3}}{3}$

$\frac{x^{3}}{3}$

The integral of a function times a constant ($2$) is equal to the constant times the integral of the function

$2\int xdx$

Applying the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a number or constant function, in this case $n=1$

$1x^2$

Any expression multiplied by $1$ is equal to itself

$x^2$
4

The integral $\int2xdx$ results in: $x^2$

$x^2$

The integral of a constant is equal to the constant times the integral's variable

$x$
5

The integral $\int1dx$ results in: $x$

$x$
6

Gather the results of all integrals

$\frac{x^{3}}{3}+x^2+x$
7

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$

$\frac{x^{3}}{3}+x^2+x+C_0$

$\frac{x^{3}}{3}+x^2+x+C_0$