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

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

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integral of (x+1)(x+2)

\int (x + 1) (x + 2) d x

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

Solution steps

\int (x + 1) (x + 2) d x

Expand

(x + 1) (x + 2) : x^{2} + 3 x + 2

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

x \to 1 lim (\frac{1}{x + 1})

f (x) = x^{2}, x = 0, x = 2

\frac{6 e ^{s} s - 5 e ^{s}}{( 6 s + 1 ) ^{2}}

\int \frac{x ^{3} + 22}{x ^{2} + 7 x + 12} d x

y = 3 e^{x} + x, (0, 3)

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