Evaluate the Integral integral of (m^4+5m) with respect to m

$\int (m^{4} + 5 m) d m$

Step 1

Remove parentheses.

$\int m^{4} + 5 m d m$

Step 2

Split the single integral into multiple integrals.

$\int m^{4} d m + \int 5 m d m$

Step 3

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

$\frac{1}{5} m^{5} + C + \int 5 m d m$

Step 4

Since $5$ is constant with respect to $m$ , move $5$ out of the integral.

$\frac{1}{5} m^{5} + C + 5 \int m d m$

Step 5

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

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

Step 6

Simplify.

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

Combine $5$ and $\frac{1}{2}$ .

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