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

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

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)

Simplify

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

= z cos (3 z)

Add a constant to the solution

= z cos (3 z) + C

\int (8 x^{3} - 9 x^{2} + 10) d x

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

\int \frac{1}{x} arcsin (x) d x

\int \frac{sin ( x )}{( 1 + sin ( x ) )} d x

\int 8 x^{3} - 6 x^{- 2} d x

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