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

The integral of (2x-5)(3x+2) is 2x^3+2x^2-(15x^2)/2-10x+C

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

\int (2 x - 5) (3 x + 2) d x

2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x + C

Solution steps

\int (2 x - 5) (3 x + 2) d x

Apply Integration By Parts

: 3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - \int 3 x^{2} + 4 x d x

= 3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - \int 3 x^{2} + 4 x d x

\int 3 x^{2} + 4 x d x = x^{3} + 2 x^{2}

= 3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - (x^{3} + 2 x^{2})

Simplify

3 x^{3} + 4 x^{2} - \frac{15 x ^{2}}{2} - 10 x - (x^{3} + 2 x^{2}) : 2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x

= 2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x

Add a constant to the solution

= 2 x^{3} + 2 x^{2} - \frac{15 x ^{2}}{2} - 10 x + C

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What is the integral of (2x-5)(3x+2) ?
The integral of (2x-5)(3x+2) is 2x^3+2x^2-(15x^2)/2-10x+C