What is the integral of (x+6)(x-5) ?

The integral of (x+6)(x-5) is (x^3)/3+(x^2)/2-30x+C

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integral of (x+6)(x-5)

\int (x + 6) (x - 5) d x

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 30 x + C

Solution steps

\int (x + 6) (x - 5) d x

Expand

(x + 6) (x - 5) : x^{2} + x - 30

= \int x^{2} + x - 30 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 x^{2} d x + \int x d x - \int 30 d x

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

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

\int 30 d x = 30 x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 30 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} - 30 x + C

\frac{d}{d x} (sin (tan (cos (2 π x^{4}))))

x \to - \infty lim (x ln (x))

\frac{d}{d x} (\frac{x - 1}{x + 1})

\frac{d}{d x} (x^{2} + x^{2} ln (x))

\frac{d y}{d t} = t^{4} y

What is the integral of (x+6)(x-5) ?
The integral of (x+6)(x-5) is (x^3)/3+(x^2)/2-30x+C