Calculus Examples

$\int (25 x^{4} + x) d x$

Step 1

Remove parentheses.

$\int 25 x^{4} + x d x$

Step 2

Split the single integral into multiple integrals.

$\int 25 x^{4} d x + \int x d x$

Step 3

Since $25$ is constant with respect to $x$ , move $25$ out of the integral.

$25 \int x^{4} d x + \int x d x$

Step 4

By the Power Rule, the integral of $x^{4}$ with respect to $x$ is $\frac{1}{5} x^{5}$ .

$25 (\frac{1}{5} x^{5} + C) + \int x d x$

Step 5

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$25 (\frac{1}{5} x^{5} + C) + \frac{1}{2} x^{2} + C$

Step 6

Simplify.

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Step 6.1

Combine $\frac{1}{5}$ and $x^{5}$ .

$25 (\frac{x^{5}}{5} + C) + \frac{1}{2} x^{2} + C$

Step 6.2

Simplify.

$5 x^{5} + \frac{1}{2} x^{2} + C$