What is the integral of (x-5)(3x+4) ?

The integral of (x-5)(3x+4) is (3x+4)((x^2)/2-5x)-3((x^3)/6-(5x^2)/2)+C

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integral of (x-5)(3x+4)

\int (x - 5) (3 x + 4) d x

(3 x + 4) (\frac{x ^{2}}{2} - 5 x) - 3 (\frac{x ^{3}}{6} - \frac{5 x ^{2}}{2}) + C

Solution steps

\int (x - 5) (3 x + 4) d x

Apply Integration By Parts

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

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

\int 3 (\frac{x ^{2}}{2} - 5 x) d x = 3 (\frac{x ^{3}}{6} - \frac{5 x ^{2}}{2})

= (3 x + 4) (\frac{x ^{2}}{2} - 5 x) - 3 (\frac{x ^{3}}{6} - \frac{5 x ^{2}}{2})

Add a constant to the solution

= (3 x + 4) (\frac{x ^{2}}{2} - 5 x) - 3 (\frac{x ^{3}}{6} - \frac{5 x ^{2}}{2}) + C

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\int 2 16 - x^{2} d x

What is the integral of (x-5)(3x+4) ?
The integral of (x-5)(3x+4) is (3x+4)((x^2)/2-5x)-3((x^3)/6-(5x^2)/2)+C