Calculus Examples

$3 e^{t} + 2 \sin (t)$

Step 1

Split the single integral into multiple integrals.

$\int 3 e^{t} d t + \int 2 \sin (t) d t$

Step 2

Since $3$ is constant with respect to $t$ , move $3$ out of the integral.

$3 \int e^{t} d t + \int 2 \sin (t) d t$

Step 3

The integral of $e^{t}$ with respect to $t$ is $e^{t}$ .

$3 (e^{t} + C) + \int 2 \sin (t) d t$

Step 4

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

$3 (e^{t} + C) + 2 \int \sin (t) d t$

Step 5

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

$3 (e^{t} + C) + 2 (- \cos (t) + C)$

Step 6

Simplify.

$3 e^{t} - 2 \cos (t) + C$