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

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

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

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

x^{3} - \frac{x ^{3}}{3} + 2 x^{2} + \frac{5 x ^{2}}{2} + 10 x + C

Solution steps

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

Apply Integration By Parts

: x^{3} + 4 x^{2} + \frac{5 x ^{2}}{2} + 10 x - \int x^{2} + 4 x d x

= x^{3} + 4 x^{2} + \frac{5 x ^{2}}{2} + 10 x - \int x^{2} + 4 x d x

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

= x^{3} + 4 x^{2} + \frac{5 x ^{2}}{2} + 10 x - (\frac{x ^{3}}{3} + 2 x^{2})

Simplify

= x^{3} - \frac{x ^{3}}{3} + 2 x^{2} + \frac{5 x ^{2}}{2} + 10 x

Add a constant to the solution

= x^{3} - \frac{x ^{3}}{3} + 2 x^{2} + \frac{5 x ^{2}}{2} + 10 x + C

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