What is the integral of 13ycos(3x)+3sin(y) ?

The integral of 13ycos(3x)+3sin(y) is 3sin(y)x+13/3 ysin(3x)+C

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integral of 13ycos(3x)+3sin(y)

\int 13 y cos (3 x) + 3 sin (y) d x

3 sin (y) x + \frac{13}{3} y sin (3 x) + C

Solution steps

\int 13 y cos (3 x) + 3 sin (y) d x

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 sin (y) d x + \int 13 cos (3 x) y d x

\int 3 sin (y) d x = 3 sin (y) x

\int 13 cos (3 x) y d x = \frac{13}{3} y sin (3 x)

= 3 sin (y) x + \frac{13}{3} y sin (3 x)

Add a constant to the solution

= 3 sin (y) x + \frac{13}{3} y sin (3 x) + C

What is the integral of 13ycos(3x)+3sin(y) ?
The integral of 13ycos(3x)+3sin(y) is 3sin(y)x+13/3 ysin(3x)+C