What is the integral of sin(3x)cos^4(3x) ?

The integral of sin(3x)cos^4(3x) is -1/15 cos^5(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(3x)cos^4(3x)

\int sin (3 x) cos^{4} (3 x) d x

- \frac{1}{15} cos^{5} (3 x) + C

Solution steps

\int sin (3 x) cos^{4} (3 x) d x

Apply u-substitution

: \int sin (u) cos^{4} (u) \frac{1}{3} d u

= \int sin (u) cos^{4} (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int sin (u) cos^{4} (u) d u

Apply u-substitution

: \int - v^{4} d v

= \frac{1}{3} \cdot \int - v^{4} d v

Take the constant out:

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

= \frac{1}{3} (- \int v^{4} d v)

Apply the Power Rule

: \frac{v ^{5}}{5}

= \frac{1}{3} (- \frac{v ^{5}}{5})

Substitute back

= \frac{1}{3} (- \frac{cos ^{5} ( 3 x )}{5})

Simplify

\frac{1}{3} (- \frac{cos ^{5} ( 3 x )}{5}) : - \frac{1}{15} cos^{5} (3 x)

= - \frac{1}{15} cos^{5} (3 x)

Add a constant to the solution

= - \frac{1}{15} cos^{5} (3 x) + C

\int (7 x - 1) e^{2 x} d x

\int 0.04 x + 27 d x

\int x tan^{2} (x^{2}) sec^{2} (x^{2}) d x

3

\int \frac{e ^{2 x} - e ^{3 x}}{e ^{x}} d x

What is the integral of sin(3x)cos^4(3x) ?
The integral of sin(3x)cos^4(3x) is -1/15 cos^5(3x)+C