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

The integral of sin(x)sqrt(cos(x)-1) is -2/3 (cos(x)-1)^{3/2}+C

Popular >

integral of sin(x)sqrt(cos(x)-1)

\int sin (x) cos (x) - 1 d x

- \frac{2}{3} (cos (x) - 1)^{\frac{3}{2}} + C

Solution steps

\int sin (x) cos (x) - 1 d x

Apply u-substitution

: \int - u - 1 d u

= \int - u - 1 d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u - 1 d u

Apply u-substitution

: \int v d v

= - \int v d v

Apply the Power Rule

: \frac{2}{3} v^{\frac{3}{2}}

= - \frac{2}{3} v^{\frac{3}{2}}

Substitute back

= - \frac{2}{3} (cos (x) - 1)^{\frac{3}{2}}

Add a constant to the solution

= - \frac{2}{3} (cos (x) - 1)^{\frac{3}{2}} + C

\int (\frac{p}{2 x ^{2}} + pq) d x

\int sin (3 x + 7) d x

\int \frac{e ^{2 x}}{7 - 4 e ^{2 x}} d x

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

\int (2 x^{3} + \frac{3}{x ^{2}} + 8 e^{x}) d x

What is the integral of sin(x)sqrt(cos(x)-1) ?
The integral of sin(x)sqrt(cos(x)-1) is -2/3 (cos(x)-1)^{3/2}+C