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

The integral of (2sin(x)cos(x)) is 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 (2sin(x)cos(x))

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

sin^{2} (x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= 2 \cdot \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Simplify

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

= sin^{2} (x)

Add a constant to the solution

= sin^{2} (x) + C

\int 7 tan^{5} (x) d x

f (x) = x + sin (x)

\int y e^{x} d x

\int \frac{e ^{8 x}}{e ^{8 x} + 9} d x

\frac{d}{d x} ((8 x^{2} - 13 x) e^{x})

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