What is the integral of sin(2x)sqrt(2+sin^2(x)) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(2x)sqrt(2+sin^2(x))

\int sin (2 x) 2 + sin^{2} (x) d x

\frac{2}{3} (2 + sin^{2} (x))^{\frac{3}{2}} + C

Solution steps

\int sin (2 x) 2 + sin^{2} (x) d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 2 + sin^{2} (x)

= \frac{2}{3} (2 + sin^{2} (x))^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (2 + sin^{2} (x))^{\frac{3}{2}} + C

\int \frac{4 x + 1}{4 x} d x

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

\int 3 e^{x} + π^{2} d x

\int - \frac{8}{x ^{6}} d x

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

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