What is the integral of sin^2(x)cos(y) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin^2(x)cos(y)

\int sin^{2} (x) cos (y) d x

cos (y) \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

Solution steps

\int sin^{2} (x) cos (y) d x

Take the constant out:

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

= cos (y) \cdot \int sin^{2} (x) d x

Rewrite using trig identities

= cos (y) \cdot \int \frac{1 - cos ( 2 x )}{2} d x

Take the constant out:

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

= cos (y) \frac{1}{2} \cdot \int 1 - cos (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= cos (y) \frac{1}{2} (\int 1 d x - \int cos (2 x) d x)

\int 1 d x = x

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

= cos (y) \frac{1}{2} (x - \frac{1}{2} sin (2 x))

Add a constant to the solution

= cos (y) \frac{1}{2} (x - \frac{1}{2} sin (2 x)) + C

\int \frac{1}{2} x cos (16 π x^{2}) d x

\int 3 tan (2 x) ln (sec (2 x)) d x

\int \frac{x x}{1 + x ^{2} x} d x

\int \frac{2 x ^{2}}{8 + x ^{2}} d x

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

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