What is the integral of 12x^2(4x^3-3) ?

The integral of 12x^2(4x^3-3) is 12(4/3 x^6-x^3-(2x^6)/3)+C

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integral of 12x^2(4x^3-3)

\int 12 x^{2} (4 x^{3} - 3) d x

12 (\frac{4}{3} x^{6} - x^{3} - \frac{2 x ^{6}}{3}) + C

Solution steps

\int 12 x^{2} (4 x^{3} - 3) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 12 \cdot \int x^{2} (4 x^{3} - 3) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} (4 x^{3} - 3) - \int 4 x^{5} d x

= 12 (\frac{1}{3} x^{3} (4 x^{3} - 3) - \int 4 x^{5} d x)

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

= 12 (\frac{1}{3} x^{3} (4 x^{3} - 3) - \frac{2 x ^{6}}{3})

Expand

\frac{1}{3} x^{3} (4 x^{3} - 3) : \frac{4}{3} x^{6} - x^{3}

= 12 (\frac{4}{3} x^{6} - x^{3} - \frac{2 x ^{6}}{3})

Add a constant to the solution

= 12 (\frac{4}{3} x^{6} - x^{3} - \frac{2 x ^{6}}{3}) + C

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What is the integral of 12x^2(4x^3-3) ?
The integral of 12x^2(4x^3-3) is 12(4/3 x^6-x^3-(2x^6)/3)+C