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

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

Popular >

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

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

\frac{x ^{7}}{7} - 2 x - \frac{1}{5 x ^{5}} + C

Solution steps

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

Simplify

(x^{3} - \frac{1}{x ^{3}})^{2} : x^{6} - 2 + \frac{1}{x ^{6}}

= \int x^{6} - 2 + \frac{1}{x ^{6}} 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 2 d x + \int \frac{1}{x ^{6}} d x

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

\int 2 d x = 2 x

\int \frac{1}{x ^{6}} d x = - \frac{1}{5 x ^{5}}

= \frac{x ^{7}}{7} - 2 x - \frac{1}{5 x ^{5}}

Add a constant to the solution

= \frac{x ^{7}}{7} - 2 x - \frac{1}{5 x ^{5}} + C

\int x (1 + 2 x^{4}) d x

\frac{\partial}{\partial x} (4 x^{3} y^{2} + 3)

y = ln (2 x + 1)

\frac{d}{d x} (lo g_{2} (2 x^{2} - 7 x + 1))

\int 4 x e^{9 x} d x

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