What is the integral of (2x-5)(3x+1) ?

The integral of (2x-5)(3x+1) is 2x^3-(13x^2)/2-5x+C

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integral of (2x-5)(3x+1)

\int (2 x - 5) (3 x + 1) d x

2 x^{3} - \frac{13 x ^{2}}{2} - 5 x + C

Solution steps

\int (2 x - 5) (3 x + 1) d x

Expand

(2 x - 5) (3 x + 1) : 6 x^{2} - 13 x - 5

= \int 6 x^{2} - 13 x - 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 x^{2} d x - \int 13 x d x - \int 5 d x

\int 6 x^{2} d x = 2 x^{3}

\int 13 x d x = \frac{13 x ^{2}}{2}

\int 5 d x = 5 x

= 2 x^{3} - \frac{13 x ^{2}}{2} - 5 x

Add a constant to the solution

= 2 x^{3} - \frac{13 x ^{2}}{2} - 5 x + C

x \to 0 lim (2 x)

\int \frac{1}{2 + 9 x ^{2}} d x

\frac{d y}{d x} = 9 x

\int \frac{y}{1 + y} d y

\int sec (3 x) d x

What is the integral of (2x-5)(3x+1) ?
The integral of (2x-5)(3x+1) is 2x^3-(13x^2)/2-5x+C