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

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

Popular >

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

\int (x + 1)^{2} \cdot x^{2} d x

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

Solution steps

\int (x + 1)^{2} x^{2} d x

Expand

(x + 1)^{2} x^{2} : x^{4} + 2 x^{3} + x^{2}

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

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

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

Add a constant to the solution

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

f (x) = 5 (9 x^{7} + 3 x^{4} - 2)^{3}

\frac{d}{d x} (3^{x l o g_{2} (x^{4})})

\frac{d}{d x} (ln (n x + 10))

x \to 0 + lim (x^{\frac{4}{x}})

x \to 0 lim (sin (7 x))

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