What is the integral of (x+1)(x+4) ?

The integral of (x+1)(x+4) is (x^3)/3+(5x^2)/2+4x+C

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integral of (x+1)(x+4)

\int (x + 1) (x + 4) d x

\frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + 4 x + C

Solution steps

\int (x + 1) (x + 4) d x

Expand

(x + 1) (x + 4) : x^{2} + 5 x + 4

= \int x^{2} + 5 x + 4 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 5 x d x + \int 4 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 d x = 4 x

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{5 x ^{2}}{2} + 4 x + C

\int \frac{1}{x x ^{2} - a ^{2}} d x

x \to 6 lim (2 x)

\frac{\partial}{\partial y} (2 x y)

\frac{d}{d x} (\frac{2 π - x cos ( x )}{x - 2 π})

\frac{d}{d x} (7 e^{x^{2} + 1})

What is the integral of (x+1)(x+4) ?
The integral of (x+1)(x+4) is (x^3)/3+(5x^2)/2+4x+C