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

The integral of (x^3+1)^3 is (x^{10}}{10}+\frac{3x^7)/7+(3x^4)/4+x+C

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integral of (x^3+1)^3

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

\frac{x ^{10}}{10} + \frac{3 x ^{7}}{7} + \frac{3 x ^{4}}{4} + x + C

Solution steps

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

Expand

(x^{3} + 1)^{3} : x^{9} + 3 x^{6} + 3 x^{3} + 1

= \int x^{9} + 3 x^{6} + 3 x^{3} + 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^{9} d x + \int 3 x^{6} d x + \int 3 x^{3} d x + \int 1 d x

\int x^{9} d x = \frac{x ^{10}}{10}

\int 3 x^{6} d x = \frac{3 x ^{7}}{7}

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

\int 1 d x = x

= \frac{x ^{10}}{10} + \frac{3 x ^{7}}{7} + \frac{3 x ^{4}}{4} + x

Add a constant to the solution

= \frac{x ^{10}}{10} + \frac{3 x ^{7}}{7} + \frac{3 x ^{4}}{4} + x + C

f (x) = \frac{8}{7 x ^{2}}

f (x) = x^{2} - 2 x + 1

\frac{d}{d x} ((2 x^{2} - 4 x)^{- 2})

x \to \infty lim ((x)^{2})

k = 0 \sum \infty \frac{3 ^{k}}{k !}

What is the integral of (x^3+1)^3 ?
The integral of (x^3+1)^3 is (x^{10}}{10}+\frac{3x^7)/7+(3x^4)/4+x+C