What is the integral of 9xsin(2-3x) ?

The integral of 9xsin(2-3x) is 3xcos(2-3x)+sin(2-3x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 9xsin(2-3x)

\int 9 x sin (2 - 3 x) d x

3 x cos (2 - 3 x) + sin (2 - 3 x) + C

Solution steps

\int 9 x sin (2 - 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 sin (2 - 3 x) d x

Apply Integration By Parts

: \frac{1}{3} x cos (2 - 3 x) - \int \frac{1}{3} cos (2 - 3 x) d x

= 9 (\frac{1}{3} x cos (2 - 3 x) - \int \frac{1}{3} cos (2 - 3 x) d x)

\int \frac{1}{3} cos (2 - 3 x) d x = - \frac{1}{9} sin (2 - 3 x)

= 9 (\frac{1}{3} x cos (2 - 3 x) - (- \frac{1}{9} sin (2 - 3 x)))

Simplify

9 (\frac{1}{3} x cos (2 - 3 x) - (- \frac{1}{9} sin (2 - 3 x))) : 3 x cos (2 - 3 x) + sin (2 - 3 x)

= 3 x cos (2 - 3 x) + sin (2 - 3 x)

Add a constant to the solution

= 3 x cos (2 - 3 x) + sin (2 - 3 x) + C

\int \frac{x ^{3} + 5 x ^{2} + 9 x + 7}{x ^{2} + 5 x + 4} d x

\int \frac{1}{x e ^{x}} d x

\int \frac{cot ^{3} ( x )}{csc ( x )} d x

\int \frac{1}{( 64 - x ^{2} ) ^{3}} d x

\int sin (2 π x) d x

What is the integral of 9xsin(2-3x) ?
The integral of 9xsin(2-3x) is 3xcos(2-3x)+sin(2-3x)+C