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

The integral of (x^2+1)^3 is (x^7)/7+(3x^5)/5+x^3+x+C

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integral of (x^2+1)^3

integral

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

\frac{x ^{7}}{7} + \frac{3 x ^{5}}{5} + x^{3} + x + C

Solution steps

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

Expand

(x^{2} + 1)^{3} : x^{6} + 3 x^{4} + 3 x^{2} + 1

= \int x^{6} + 3 x^{4} + 3 x^{2} + 1 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^{6} d x + \int 3 x^{4} d x + \int 3 x^{2} d x + \int 1 d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

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

\int 1 d x = x

= \frac{x ^{7}}{7} + \frac{3 x ^{5}}{5} + x^{3} + x

Add a constant to the solution

= \frac{x ^{7}}{7} + \frac{3 x ^{5}}{5} + x^{3} + x + C

ln (x - 1)

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

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

sin (\frac{x}{3})

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

What is the integral of (x^2+1)^3 ?
The integral of (x^2+1)^3 is (x^7)/7+(3x^5)/5+x^3+x+C