Calculus Examples

$\int 2 u^{2} - 2 u^{- 1} d u$

Step 1

Split the single integral into multiple integrals.

$\int 2 u^{2} d u + \int - 2 u^{- 1} d u$

Step 2

Since $2$ is constant with respect to $u$ , move $2$ out of the integral.

$2 \int u^{2} d u + \int - 2 u^{- 1} d u$

Step 3

By the Power Rule, the integral of $u^{2}$ with respect to $u$ is $\frac{1}{3} u^{3}$ .

$2 (\frac{1}{3} u^{3} + C) + \int - 2 u^{- 1} d u$

Step 4

Since $- 2$ is constant with respect to $u$ , move $- 2$ out of the integral.

$2 (\frac{1}{3} u^{3} + C) - 2 \int u^{- 1} d u$

Step 5

The integral of $u^{- 1}$ with respect to $u$ is $\ln (| u |)$ .

$2 (\frac{1}{3} u^{3} + C) - 2 (\ln (| u |) + C)$

Step 6

Simplify.

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Step 6.1

Simplify.

$2 (\frac{1}{3}) u^{3} - 2 \ln (| u |) + C$

Step 6.2

Combine $2$ and $\frac{1}{3}$ .

$\frac{2}{3} u^{3} - 2 \ln (| u |) + C$