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

The integral of 2*sin(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 \cdot sin (x) \cdot 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

\frac{d}{d x} (I n (x^{2} y))

\frac{( x ^{2} + 1 ) d y}{d x} + x y - x = 0

e^{2 t} sin (2 t)

S^{2}

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

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