Calculus Examples

$\int x - \sin (x) d x$

Step 1

Split the single integral into multiple integrals.

$\int x d x + \int - \sin (x) d x$

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify.

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

Step 5.2

Simplify.

Tap for more steps...

Step 5.2.1

Multiply $- 1$ by $- 1$ .

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

Step 5.2.2

Multiply $\cos (x)$ by $1$ .

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