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

The integral of (x^2+1)^2x is (x^6)/6+(x^4)/2+(x^2)/2+C

Popular >

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

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

\frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2} + C

Solution steps

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

Expand

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

= \int x^{5} + 2 x^{3} + x 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^{5} d x + \int 2 x^{3} d x + \int x d x

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

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

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

= \frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2}

Add a constant to the solution

= \frac{x ^{6}}{6} + \frac{x ^{4}}{2} + \frac{x ^{2}}{2} + C

ln (1 - 3 x)

\int x^{2} n^{2} xx d x

\int x (3 - x) d x

\int \frac{5 e ^{x}}{e ^{2 x} + 6 e ^{x} + 9} d x

\int_{0}^{2} (4 x - x^{3}) d x

What is the integral of (x^2+1)^2x ?
The integral of (x^2+1)^2x is (x^6)/6+(x^4)/2+(x^2)/2+C