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

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

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integral of (sin(θ))/(cos^2(θ))

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

sec (θ) + C

Solution steps

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

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 (θ)

= - (- \frac{1}{cos ( θ )})

Simplify

- (- \frac{1}{cos ( θ )}) : sec (θ)

= sec (θ)

Add a constant to the solution

= sec (θ) + C

\int \frac{( x + 2 ) ^{2}}{5 x} d x

\frac{d}{d x} (\frac{9 x}{ln ( x )})

f (x) = \frac{x + 1}{x}

(x - \frac{6}{x})^{8}

\frac{d}{d x} (\frac{3 x ^{2} + 4 x + 3}{x ^{2} + 1})

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