What is the integral of sin(x)os(x) ?

The integral of sin(x)os(x) is d/2 sin^2(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)os(x)

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

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

Solution steps

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

Take the constant out:

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

= d \cdot \int sin (x) cos (x) d x

Apply u-substitution

: \int u d u

= d \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

= d \frac{sin ^{2} ( x )}{2}

Simplify

d \frac{sin ^{2} ( x )}{2} : \frac{d}{2} sin^{2} (x)

= \frac{d}{2} sin^{2} (x)

Add a constant to the solution

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

\int 2 x 4 x - 5 d x

\int \frac{1}{( x - 2 ) x ^{2} - 4 x + 3} d x

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

\int \frac{1}{( z ^{2} - 2 z + 5 ) ^{2}} d z

\int \frac{4 x}{16 - x ^{2}} d x

What is the integral of sin(x)os(x) ?
The integral of sin(x)os(x) is d/2 sin^2(x)+C