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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of cos(x)sin(2x)

\int cos (x) sin (2 x) d x

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

Solution steps

\int cos (x) sin (2 x) d x

Rewrite using trig identities

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

Take the constant out:

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

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

Apply u-substitution

: \int - u^{2} d u

= 2 \cdot \int - u^{2} d u

Take the constant out:

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

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

Apply the Power Rule

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

= 2 (- \frac{u ^{3}}{3})

Substitute back

u = cos (x)

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

Simplify

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

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

Add a constant to the solution

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

x \to - 1 lim (\frac{x ^{7} + 1}{x + 1})

\int (x^{6} + 1) e^{x^{7} + 7 x} d x

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

f (x) = x + 5, at x = - 4

\int tan^{2} (5 x) sec^{4} (5 x) d x

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