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

The integral of (2x^3-1)^3 is (4x^{10})/5-(12x^7)/7+(3x^4)/2-x+C

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integral of (2x^3-1)^3

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

\frac{4 x ^{10}}{5} - \frac{12 x ^{7}}{7} + \frac{3 x ^{4}}{2} - x + C

Solution steps

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

Expand

(2 x^{3} - 1)^{3} : 8 x^{9} - 12 x^{6} + 6 x^{3} - 1

= \int 8 x^{9} - 12 x^{6} + 6 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 8 x^{9} d x - \int 12 x^{6} d x + \int 6 x^{3} d x - \int 1 d x

\int 8 x^{9} d x = \frac{4 x ^{10}}{5}

\int 12 x^{6} d x = \frac{12 x ^{7}}{7}

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

\int 1 d x = x

= \frac{4 x ^{10}}{5} - \frac{12 x ^{7}}{7} + \frac{3 x ^{4}}{2} - x

Add a constant to the solution

= \frac{4 x ^{10}}{5} - \frac{12 x ^{7}}{7} + \frac{3 x ^{4}}{2} - x + C

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What is the integral of (2x^3-1)^3 ?
The integral of (2x^3-1)^3 is (4x^{10})/5-(12x^7)/7+(3x^4)/2-x+C