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

The integral of cos(x)*sin(x) is (sin^2(x))/2+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(x)

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

\int x cos^{4} (x^{2}) d x

y^{^{''}} + 4 y^{^{'}} + 4 y = 3 e^{- 2 t}

x^{'} (t) = \frac{1}{3 x ^{2} + 1}, x (0) = 1

\frac{\partial}{\partial x} (e^{- 6 t} cos (π x))

\frac{\partial}{\partial y} (9 z e^{x yz})

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