What is the integral of 3x^2(2x^2-5) ?

The integral of 3x^2(2x^2-5) is 2x^5-5x^3-(4x^5)/5+C

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integral of 3x^2(2x^2-5)

\int 3 x^{2} (2 x^{2} - 5) d x

2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5} + C

Solution steps

\int 3 x^{2} (2 x^{2} - 5) d x

Take the constant out:

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

= 3 \cdot \int x^{2} (2 x^{2} - 5) d x

Apply Integration By Parts

= 3 (\frac{1}{3} x^{3} (2 x^{2} - 5) - \int \frac{4 x ^{4}}{3} d x)

\int \frac{4 x ^{4}}{3} d x = \frac{4 x ^{5}}{15}

= 3 (\frac{1}{3} x^{3} (2 x^{2} - 5) - \frac{4 x ^{5}}{15})

Simplify

3 (\frac{1}{3} x^{3} (2 x^{2} - 5) - \frac{4 x ^{5}}{15}) : 2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5}

= 2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5}

Add a constant to the solution

= 2 x^{5} - 5 x^{3} - \frac{4 x ^{5}}{5} + C

What is the integral of 3x^2(2x^2-5) ?
The integral of 3x^2(2x^2-5) is 2x^5-5x^3-(4x^5)/5+C