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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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