What is the integral of (sin(y))/(cos^2(y)) ?

The integral of (sin(y))/(cos^2(y)) is sec(y)+C

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integral of (sin(y))/(cos^2(y))

integral

\frac{sin ( y )}{cos ^{2} ( y )}

sec (y) + C

Solution steps

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

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= \int - \frac{1}{u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = cos (y)

= - (- \frac{1}{cos ( y )})

Simplify

- (- \frac{1}{cos ( y )}) : sec (y)

= sec (y)

Add a constant to the solution

= sec (y) + C

tan (x) + \frac{1}{x}

e^{\frac{- y}{2}}

\frac{e ^{2} x}{2}

1 - tan^{2} (x)

\frac{x ^{3}}{( x + 2 ) ^{4}}

What is the integral of (sin(y))/(cos^2(y)) ?
The integral of (sin(y))/(cos^2(y)) is sec(y)+C