What is the integral of 9xcos(3x) ?

The integral of 9xcos(3x) is 3xsin(3x)+cos(3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 9xcos(3x)

\int 9 x cos (3 x) d x

3 x sin (3 x) + cos (3 x) + C

Solution steps

\int 9 x cos (3 x) d x

Take the constant out:

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

= 9 \cdot \int x cos (3 x) d x

Apply u-substitution

: \int \frac{u cos ( u )}{9} d u

= 9 \cdot \int \frac{u cos ( u )}{9} d u

Take the constant out:

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

= 9 \cdot \frac{1}{9} \cdot \int u cos (u) d u

Apply Integration By Parts

: u sin (u) - \int sin (u) d u

= 9 \cdot \frac{1}{9} (u sin (u) - \int sin (u) d u)

\int sin (u) d u = - cos (u)

= 9 \cdot \frac{1}{9} (u sin (u) - (- cos (u)))

Substitute back

u = 3 x

= 9 \cdot \frac{1}{9} (3 x sin (3 x) - (- cos (3 x)))

Simplify

9 \cdot \frac{1}{9} (3 x sin (3 x) - (- cos (3 x))) : 3 x sin (3 x) + cos (3 x)

= 3 x sin (3 x) + cos (3 x)

Add a constant to the solution

= 3 x sin (3 x) + cos (3 x) + C

\int e^{- x} \cdot cos (2 x) d x

\frac{d}{d x} (- sin (x))

n = 1 \sum \infty \frac{n ^{4}}{n !}

\int_{0}^{9} \frac{1}{3} x - 2 d x

\int \frac{4 - 4 x}{1 - x} d x

What is the integral of 9xcos(3x) ?
The integral of 9xcos(3x) is 3xsin(3x)+cos(3x)+C