What is the integral of (x^4+3x)^2 ?

The integral of (x^4+3x)^2 is (x^9)/9+x^6+3x^3+C

Popular >

integral of (x^4+3x)^2

\int (x^{4} + 3 x)^{2} d x

\frac{x ^{9}}{9} + x^{6} + 3 x^{3} + C

Solution steps

\int (x^{4} + 3 x)^{2} d x

Expand

(x^{4} + 3 x)^{2} : x^{8} + 6 x^{5} + 9 x^{2}

= \int x^{8} + 6 x^{5} + 9 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^{8} d x + \int 6 x^{5} d x + \int 9 x^{2} d x

\int x^{8} d x = \frac{x ^{9}}{9}

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

\int 9 x^{2} d x = 3 x^{3}

= \frac{x ^{9}}{9} + x^{6} + 3 x^{3}

Add a constant to the solution

= \frac{x ^{9}}{9} + x^{6} + 3 x^{3} + C

x \to 1 lim (x^{3} + x^{2} - 3)

\int_{1}^{32} (x^{- \frac{6}{5}}) d x

f (x) = 3 x + 13, (12, 7)

y = 3 (ln (x) + 1)

\frac{d}{d x} (2 cos (5 x))

What is the integral of (x^4+3x)^2 ?
The integral of (x^4+3x)^2 is (x^9)/9+x^6+3x^3+C