Calculus Examples

$2 x^{2} - \cos (x)$

Step 1

Split the single integral into multiple integrals.

$\int 2 x^{2} d x + \int - \cos (x) d x$

Step 2

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

$2 \int x^{2} d x + \int - \cos (x) d x$

Step 3

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

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

Step 4

Since $- 1$ is constant with respect to $x$ , move $- 1$ out of the integral.

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

Step 5

The integral of $\cos (x)$ with respect to $x$ is $\sin (x)$ .

$2 (\frac{1}{3} x^{3} + C) - (\sin (x) + C)$

Step 6

Simplify.

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Step 6.1

Simplify.

$2 (\frac{1}{3}) x^{3} - \sin (x) + C$

Step 6.2

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

$\frac{2}{3} x^{3} - \sin (x) + C$