What is the integral of (3x^2ln(4x)+x^2) ?

The integral of (3x^2ln(4x)+x^2) is x^3ln(4x)+C

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integral of (3x^2ln(4x)+x^2)

\int (3 x^{2} ln (4 x) + x^{2}) d x

x^{3} ln (4 x) + C

Solution steps

\int 3 x^{2} ln (4 x) + 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 3 x^{2} ln (4 x) d x + \int x^{2} d x

\int 3 x^{2} ln (4 x) d x = x^{3} ln (4 x) - \frac{x ^{3}}{3}

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

= x^{3} ln (4 x) - \frac{x ^{3}}{3} + \frac{x ^{3}}{3}

Simplify

= x^{3} ln (4 x)

Add a constant to the solution

= x^{3} ln (4 x) + C

What is the integral of (3x^2ln(4x)+x^2) ?
The integral of (3x^2ln(4x)+x^2) is x^3ln(4x)+C