What is the integral of 6xsin^2(x)cos(x) ?

The integral of 6xsin^2(x)cos(x) is 6(1/3 xsin^3(x)-1/3 (-cos(x)+(cos^3(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 6xsin^2(x)cos(x)

\int 6 x sin^{2} (x) cos (x) d x

6 (\frac{1}{3} x sin^{3} (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})) + C

Solution steps

\int 6 x sin^{2} (x) cos (x) d x

Take the constant out:

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

= 6 \cdot \int x sin^{2} (x) cos (x) d x

Apply Integration By Parts

: \frac{1}{3} x sin^{3} (x) - \int \frac{1}{3} sin^{3} (x) d x

= 6 (\frac{1}{3} x sin^{3} (x) - \int \frac{1}{3} sin^{3} (x) d x)

\int \frac{1}{3} sin^{3} (x) d x = \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})

= 6 (\frac{1}{3} x sin^{3} (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3}))

Add a constant to the solution

= 6 (\frac{1}{3} x sin^{3} (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})) + C

\int \frac{cos ( x )}{( 1 + sin ^{2} ( x ) )} d x

\int 4 y - 1 d y

\int sin (x y) d x

\int e^{3 - 8 x} d x

\int - 4 sin (t) d t

What is the integral of 6xsin^2(x)cos(x) ?
The integral of 6xsin^2(x)cos(x) is 6(1/3 xsin^3(x)-1/3 (-cos(x)+(cos^3(x))/3))+C