What is the integral of (sin(x))/(sqrt(1-cos^2(x))) ?

The integral of (sin(x))/(sqrt(1-cos^2(x))) is arcsin(sin(x))+C

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integral of (sin(x))/(sqrt(1-cos^2(x)))

\int \frac{sin ( x )}{1 - cos ^{2} ( x )} d x

arcsin (sin (x)) + C

Solution steps

\int \frac{sin ( x )}{1 - cos ^{2} ( x )} d x

Apply u-substitution

: \int \frac{1}{1 - u ^{2}} d u

= \int \frac{1}{1 - u ^{2}} d u

Use the common integral:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= arcsin (u)

Substitute back

u = sin (x)

= arcsin (sin (x))

Add a constant to the solution

= arcsin (sin (x)) + C

- 3 x^{2} - 10 x, 3

\int \frac{3 x ^{2}}{x} d x

\int_{0}^{1} \frac{6}{x ^{2} + 2 x - 8} d x

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

x \to 0 lim (\frac{( 3 + x ) - ( 3 )}{x})

What is the integral of (sin(x))/(sqrt(1-cos^2(x))) ?
The integral of (sin(x))/(sqrt(1-cos^2(x))) is arcsin(sin(x))+C