What is the integral of (3x^2+ycos(x)) ?

The integral of (3x^2+ycos(x)) is x^3+ysin(x)+C

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integral of (3x^2+ycos(x))

\int (3 x^{2} + y cos (x)) d x

x^{3} + y sin (x) + C

Solution steps

\int 3 x^{2} + y cos (x) 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 x^{2} d x + \int cos (x) y d x

\int 3 x^{2} d x = x^{3}

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

= x^{3} + y sin (x)

Add a constant to the solution

= x^{3} + y sin (x) + C

What is the integral of (3x^2+ycos(x)) ?
The integral of (3x^2+ycos(x)) is x^3+ysin(x)+C