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

The integral of 3x^2+3x^2ln(y) is x^3+x^3ln(y)+C

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integral of 3x^2+3x^2ln(y)

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

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

Solution steps

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

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

\int 3 ln (y) x^{2} d x = x^{3} ln (y)

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

Add a constant to the solution

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

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What is the integral of 3x^2+3x^2ln(y) ?
The integral of 3x^2+3x^2ln(y) is x^3+x^3ln(y)+C