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

The integral of (x^3)/2+1/(2x^3) is (x^4)/8-1/(4x^2)+C

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

\int \frac{x ^{3}}{2} + \frac{1}{2 x ^{3}} d x

\frac{x ^{4}}{8} - \frac{1}{4 x ^{2}} + C

Solution steps

\int \frac{x ^{3}}{2} + \frac{1}{2 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 \frac{x ^{3}}{2} d x + \int \frac{1}{2 x ^{3}} d x

\int \frac{x ^{3}}{2} d x = \frac{x ^{4}}{8}

\int \frac{1}{2 x ^{3}} d x = - \frac{1}{4 x ^{2}}

= \frac{x ^{4}}{8} - \frac{1}{4 x ^{2}}

Add a constant to the solution

= \frac{x ^{4}}{8} - \frac{1}{4 x ^{2}} + C

\int_{0}^{\frac{π}{2}} (cos (x)) d x

\int \frac{11}{12} x^{2} + \frac{1}{12} x d x

\frac{d}{d t} (sin (t))

\int (1 - \frac{1}{x}) d x

\frac{\partial}{\partial t} (e^{- 2 t})

What is the integral of (x^3)/2+1/(2x^3) ?
The integral of (x^3)/2+1/(2x^3) is (x^4)/8-1/(4x^2)+C