What is the integral of (x+5)(4x-11) ?

The integral of (x+5)(4x-11) is (4x^3)/3+(9x^2)/2-55x+C

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integral of (x+5)(4x-11)

\int (x + 5) (4 x - 11) d x

\frac{4 x ^{3}}{3} + \frac{9 x ^{2}}{2} - 55 x + C

Solution steps

\int (x + 5) (4 x - 11) d x

Expand

(x + 5) (4 x - 11) : 4 x^{2} + 9 x - 55

= \int 4 x^{2} + 9 x - 55 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 4 x^{2} d x + \int 9 x d x - \int 55 d x

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

\int 9 x d x = \frac{9 x ^{2}}{2}

\int 55 d x = 55 x

= \frac{4 x ^{3}}{3} + \frac{9 x ^{2}}{2} - 55 x

Add a constant to the solution

= \frac{4 x ^{3}}{3} + \frac{9 x ^{2}}{2} - 55 x + C

\int \frac{13}{36 - 36 x ^{2}} d x

\frac{d}{d x} (cos (12 x))

(y + 2 x e^{- \frac{y}{x}}) d x - x d y = 0

f (x) = \frac{4 x - 5}{x}

x^{2} + 10 x + 25, - 2 x - 2, - 5, - 1

What is the integral of (x+5)(4x-11) ?
The integral of (x+5)(4x-11) is (4x^3)/3+(9x^2)/2-55x+C