What is the integral of (sin(x/3)cos(x/3)) ?

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

\int (sin (\frac{x}{3}) cos (\frac{x}{3})) d x

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

Solution steps

\int sin (\frac{x}{3}) cos (\frac{x}{3}) d x

Apply u-substitution

: \int - 3 u d u

= \int - 3 u d u

Take the constant out:

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

= - 3 \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = cos (\frac{x}{3})

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

Simplify

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

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

Add a constant to the solution

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

\int r ln (\frac{2 r}{g}) d r

\int (x^{4} - 2 x)^{5} (2 x^{3} - 1) d x

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

\int (cos (x) + x) d x

\int \frac{1 + x ^{2}}{x ^{4}} d x

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