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Popular >

integral of csc(θ)

Solution

\int csc (θ) d θ

Solution

ln tan (\frac{θ}{2}) + C

Solution steps

\int csc (θ) d θ

Apply u-substitution

: \int \frac{1}{u} d u

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = tan (\frac{θ}{2})

= ln tan (\frac{θ}{2})

Add a constant to the solution

= ln tan (\frac{θ}{2}) + C

Popular Examples

limit as x approaches+3 of 6

x \to + 3 lim (6)

integral of θ^3cos(θ)

\int θ^{3} cos (θ) d θ

integral from 0 to pi/3 of 2+sin(3x)

\int_{0}^{\frac{π}{3}} 2 + sin (3 x) d x

integral of e^{-iwx}

\int e^{- i w x} d x

(x-1)y^'+y(x-2)=0

(x - 1) y^{^{'}} + y (x - 2) = 0

Frequently Asked Questions (FAQ)

What is the integral of csc(θ) ?
The integral of csc(θ) is ln|tan(θ/2)|+C