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Popular >

integral of csc(x)

Solution

\int csc (x) d x

Solution

ln tan (\frac{x}{2}) + C

Solution steps

\int csc (x) d x

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{x}{2})

= ln tan (\frac{x}{2})

Add a constant to the solution

= ln tan (\frac{x}{2}) + C

Popular Examples

derivative of sqrt((x^2+1^2))

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

integral of (x+1)^{10}

\int (x + 1)^{10} d x

sin(2x)dx+cos(4y)dy=0,y(pi/2)= pi/4

sin (2 x) d x + cos (4 y) d y = 0, y (\frac{π}{2}) = \frac{π}{4}

tangent of y=2x+3cos(x)tangent of

y = 2 x + 3 cos (x)

limit as x approaches 0 of f(x)

x \to 0 lim (f (x))

Frequently Asked Questions (FAQ)

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