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Popular >

integral of (sec(θ))/(cos(θ)-sec(θ))

Solution

\int \frac{sec ( θ )}{cos ( θ ) - sec ( θ )} d θ

Solution

cot (θ) + C

Solution steps

\int \frac{sec ( θ )}{cos ( θ ) - sec ( θ )} d θ

Rewrite using trig identities

= \int - \frac{1}{sin ^{2} ( θ )} d θ

Take the constant out:

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

= - \int \frac{1}{sin ^{2} ( θ )} d θ

Use the common integral:

\int \frac{1}{sin ^{2} ( θ )} d θ = - cot (θ)

= - (- cot (θ))

Simplify

= cot (θ)

Add a constant to the solution

= cot (θ) + C

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\int \frac{v ^{2}}{- v ^{2} + 3} d v

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\int sin (3 x + 4) d x

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

Frequently Asked Questions (FAQ)

What is the integral of (sec(θ))/(cos(θ)-sec(θ)) ?
The integral of (sec(θ))/(cos(θ)-sec(θ)) is cot(θ)+C