What is the integral of (2x+3/(x^2)-6/(x^4)) ?

The integral of (2x+3/(x^2)-6/(x^4)) is x^2-3/x+2/(x^3)+C

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integral of (2x+3/(x^2)-6/(x^4))

\int (2 x + \frac{3}{x ^{2}} - \frac{6}{x ^{4}}) d x

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

Solution steps

\int 2 x + \frac{3}{x ^{2}} - \frac{6}{x ^{4}} 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 d x + \int \frac{3}{x ^{2}} d x - \int \frac{6}{x ^{4}} d x

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

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

\int \frac{6}{x ^{4}} d x = - \frac{2}{x ^{3}}

= x^{2} - \frac{3}{x} - (- \frac{2}{x ^{3}})

Simplify

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

Add a constant to the solution

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

\frac{d}{d x} (sin (x) (1 + cos (x)))

\frac{d}{d x} (sin (3 x + 4 y))

\frac{d}{d x} (x^{3} + 2 x^{2} + x)

cos^{2} (z)

\int 7 x^{5} e^{- x^{3}} d x

What is the integral of (2x+3/(x^2)-6/(x^4)) ?
The integral of (2x+3/(x^2)-6/(x^4)) is x^2-3/x+2/(x^3)+C