Calculus Examples

$\int 7 \sin (z) + 6 \cos (z) d z$

Step 1

Split the single integral into multiple integrals.

$\int 7 \sin (z) d z + \int 6 \cos (z) d z$

Step 2

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

$7 \int \sin (z) d z + \int 6 \cos (z) d z$

Step 3

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

$7 (- \cos (z) + C) + \int 6 \cos (z) d z$

Step 4

Since $6$ is constant with respect to $z$ , move $6$ out of the integral.

$7 (- \cos (z) + C) + 6 \int \cos (z) d z$

Step 5

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

$7 (- \cos (z) + C) + 6 (\sin (z) + C)$

Step 6

Simplify.

$- 7 \cos (z) + 6 \sin (z) + C$