Calculus Examples

$\int (\sin (x) + 7 \cos (x) - 1) d x$

Step 1

Remove parentheses.

$\int \sin (x) + 7 \cos (x) - 1 d x$

Step 2

Split the single integral into multiple integrals.

$\int \sin (x) d x + \int 7 \cos (x) d x + \int - 1 d x$

Step 3

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

$- \cos (x) + C + \int 7 \cos (x) d x + \int - 1 d x$

Step 4

Since $7$ is constant with respect to $x$ , move $7$ out of the integral.

$- \cos (x) + C + 7 \int \cos (x) d x + \int - 1 d x$

Step 5

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

$- \cos (x) + C + 7 (\sin (x) + C) + \int - 1 d x$

Step 6

Apply the constant rule.

$- \cos (x) + C + 7 (\sin (x) + C) - x + C$

Step 7

Simplify.

$- \cos (x) + 7 \sin (x) - x + C$