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

The integral of (x^3+x+1/(x^3)) is (x^4)/4+(x^2)/2-1/(2x^2)+C

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integral of (x^3+x+1/(x^3))

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

\frac{x ^{4}}{4} + \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}} + C

Solution steps

\int x^{3} + x + \frac{1}{x ^{3}} 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^{3} d x + \int x d x + \int \frac{1}{x ^{3}} d x

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

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

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

= \frac{x ^{4}}{4} + \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{x ^{2}}{2} - \frac{1}{2 x ^{2}} + C

\int_{0}^{\frac{π}{2}} - 10 sin^{2} (3 x) d x

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

\frac{d}{d x} (tan (6 x^{2}))

\frac{\partial}{\partial x} (cos^{2} (x - y))

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

What is the integral of (x^3+x+1/(x^3)) ?
The integral of (x^3+x+1/(x^3)) is (x^4)/4+(x^2)/2-1/(2x^2)+C