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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

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

Add a constant to the solution

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

\int \frac{1}{2 x ^{2} + 4 x + 3} d x

\int \frac{x + 4}{x ^{2}} d x

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

\int \frac{2 x ^{2} + 3}{x ^{4} - 2 x ^{2} + 1} d x

\int \frac{t ^{3}}{e ^{2 t^{4}}} d t

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