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

The integral of x^2(1+x^3) is (x^3)/3+(x^6)/6+C

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integral of x^2(1+x^3)

integral

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

\frac{x ^{3}}{3} + \frac{x ^{6}}{6} + C

Solution steps

\int x^{2} (1 + x^{3}) d x

Expand

x^{2} (1 + x^{3}) : x^{2} + x^{5}

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

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

\int x^{5} d x = \frac{x ^{6}}{6}

= \frac{x ^{3}}{3} + \frac{x ^{6}}{6}

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{6}}{6} + C

\frac{1}{( x + 1 ) ( x ^{2} + 1 ) ^{2}}

d^{2} (v) v

\frac{1}{( 2 + x )}

cos (t^{3})

\frac{2 x}{( x ^{2} - a )}

What is the integral of x^2(1+x^3) ?
The integral of x^2(1+x^3) is (x^3)/3+(x^6)/6+C