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

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

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integral of 3/(2x^4)-2x

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

- \frac{1}{2 x ^{3}} - x^{2} + C

Solution steps

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

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

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

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

Add a constant to the solution

= - \frac{1}{2 x ^{3}} - x^{2} + C

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