Calculus Examples

$\int \frac{\sin (y)}{\cos^{2} (y)} d y$

Step 1

Multiply by $1$ .

$\int \frac{\sin (y) \cdot 1}{\cos^{2} (y)} d y$

Step 2

Factor $\cos (y)$ out of $\cos^{2} (y)$ .

$\int \frac{\sin (y) \cdot 1}{\cos (y) \cos (y)} d y$

Step 3

Separate fractions.

$\int \frac{\sin (y)}{\cos (y)} \cdot \frac{1}{\cos (y)} d y$

Step 4

Convert from $\frac{\sin (y)}{\cos (y)}$ to $\tan (y)$ .

$\int \tan (y) \frac{1}{\cos (y)} d y$

Step 5

Convert from $\frac{1}{\cos (y)}$ to $\sec (y)$ .

$\int \tan (y) \sec (y) d y$

Step 6

Since the derivative of $\sec (y)$ is $\tan (y) \sec (y)$ , the integral of $\tan (y) \sec (y)$ is $\sec (y)$ .

$\sec (y) + C$