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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 1+cos^2(x)derivative of

1 + cos^{2} (x)

(dx)/(dy)2-(dy)/(dx)sec(x)=0

\frac{d x}{d y} 2 - \frac{d y}{d x} sec (x) = 0

derivative of f(x)= 2/(5x+3)derivative of

f (x) = \frac{2}{5 x + 3}

sum from n=1 to infinity}((-1)^{n-1 of)/(4n+1)

n = 1 \sum \infty \frac{( - 1 ) ^{n - 1}}{4 n + 1}

derivative of (3x-2^2(2x+1)^4)

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

Frequently Asked Questions (FAQ)

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