What is the integral of (1/(sin(x))) ?

The integral of (1/(sin(x))) is ln|tan(x/2)|+C

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integral of (1/(sin(x)))

\int (\frac{1}{sin ( x )}) d x

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

Solution steps

\int \frac{1}{sin ( 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

(x + 2)^{2} + (y - 3)^{2} = 37, (- 8, 2)

f (x) = x^{3} + 2 x, at x = - 1

\frac{d}{d x} (\frac{1 + x}{1 - x})

f (x) = x ∣ x ∣

f (x) = 5 x - 4

What is the integral of (1/(sin(x))) ?
The integral of (1/(sin(x))) is ln|tan(x/2)|+C