What is the integral of 6sin^5(t)cos(t) ?

The integral of 6sin^5(t)cos(t) is sin^6(t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 6sin^5(t)cos(t)

\int 6 sin^{5} (t) cos (t) d t

sin^{6} (t) + C

Solution steps

\int 6 sin^{5} (t) cos (t) d t

Take the constant out:

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

= 6 \cdot \int sin^{5} (t) cos (t) d t

Apply u-substitution

: \int u^{5} d u

= 6 \cdot \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= 6 \cdot \frac{u ^{6}}{6}

Substitute back

u = sin (t)

= 6 \cdot \frac{sin ^{6} ( t )}{6}

Simplify

6 \cdot \frac{sin ^{6} ( t )}{6} : sin^{6} (t)

= sin^{6} (t)

Add a constant to the solution

= sin^{6} (t) + C

\frac{d}{d x} (x (x^{2} - 3))

\frac{d}{d x} (a (a - x) (a - y) (a - z))

\int 6 x - 3 d x

x^{2} + 3 x - 2, - x^{2} - 3 x + 6

n = 0 \sum \infty (\frac{3}{5})^{\frac{n}{2}}

What is the integral of 6sin^5(t)cos(t) ?
The integral of 6sin^5(t)cos(t) is sin^6(t)+C