What is the integral of 3zsin(3z)-cos(3z) ?

The integral of 3zsin(3z)-cos(3z) is -zcos(3z)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3zsin(3z)-cos(3z)

\int 3 z sin (3 z) - cos (3 z) d z

- z cos (3 z) + C

Solution steps

\int 3 z sin (3 z) - cos (3 z) d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 z sin (3 z) d z - \int cos (3 z) d z

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

\int cos (3 z) d z = \frac{1}{3} sin (3 z)

= - z cos (3 z) + \frac{1}{3} sin (3 z) - \frac{1}{3} sin (3 z)

Add similar elements:

\frac{1}{3} sin (3 z) - \frac{1}{3} sin (3 z) = 0

= - z cos (3 z)

Add a constant to the solution

= - z cos (3 z) + C

\int (2 x^{2} + 8 + \frac{6}{x ^{2} + 1}) d x

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

\int 4 x^{\frac{5}{4}} d x

\int \frac{1}{2} - x d x

\int \frac{7}{4 x ^{6}} d x

What is the integral of 3zsin(3z)-cos(3z) ?
The integral of 3zsin(3z)-cos(3z) is -zcos(3z)+C