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

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

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integral of 2x^3+1/2+1/(4x^3)

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

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

Solution steps

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

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

\int \frac{1}{2} d x = \frac{1}{2} x

\int \frac{1}{4 x ^{3}} d x = - \frac{1}{8 x ^{2}}

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

Add a constant to the solution

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

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