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))

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

x \to 2 lim (\frac{1}{3})

x^{\frac{9}{6}}, 7

x \to 0 + lim ((4 x + 1)^{c o t (x)})

\int - 2 e^{- 3 c o s (3 x)} sin (3 x) d x

\frac{\partial}{\partial x} (e^{p (x)} (p (x) + p (x) p (x)))

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