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

The integral of (4/(x^2)+2-1/(8x^3)) is -4/x+2x+1/(16x^2)+C

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

\int (\frac{4}{x ^{2}} + 2 - \frac{1}{8 x ^{3}}) d x

- \frac{4}{x} + 2 x + \frac{1}{16 x ^{2}} + C

Solution steps

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

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

\int 2 d x = 2 x

\int \frac{1}{8 x ^{3}} d x = - \frac{1}{16 x ^{2}}

= - \frac{4}{x} + 2 x - (- \frac{1}{16 x ^{2}})

Simplify

= - \frac{4}{x} + 2 x + \frac{1}{16 x ^{2}}

Add a constant to the solution

= - \frac{4}{x} + 2 x + \frac{1}{16 x ^{2}} + C

\int_{0}^{1} sin (π t) d t

\frac{d}{d x} (\frac{x}{x ^{2} + y ^{2}})

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

\frac{d}{d x} (- 4 x^{3} + 4 x)

What is the integral of (4/(x^2)+2-1/(8x^3)) ?
The integral of (4/(x^2)+2-1/(8x^3)) is -4/x+2x+1/(16x^2)+C