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

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

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integral of 3x^2+ln(x)

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

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

Solution steps

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

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

\int ln (x) d x = x ln (x) - x

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

Add a constant to the solution

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

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