What is the integral of x(60x^2+90x) ?

The integral of x(60x^2+90x) is 15x^4+30x^3+C

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integral of x(60x^2+90x)

\int x (60 x^{2} + 90 x) d x

15 x^{4} + 30 x^{3} + C

Solution steps

\int x (60 x^{2} + 90 x) d x

Expand

x (60 x^{2} + 90 x) : 60 x^{3} + 90 x^{2}

= \int 60 x^{3} + 90 x^{2} 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 60 x^{3} d x + \int 90 x^{2} d x

\int 60 x^{3} d x = 15 x^{4}

\int 90 x^{2} d x = 30 x^{3}

= 15 x^{4} + 30 x^{3}

Add a constant to the solution

= 15 x^{4} + 30 x^{3} + C

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What is the integral of x(60x^2+90x) ?
The integral of x(60x^2+90x) is 15x^4+30x^3+C