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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

\frac{d y}{d x} = e^{5 x} (cos (y))^{2}

x \to 0 lim (5 + \frac{9}{x ^{3}})

\frac{x d y}{d x} + y = 6 x + 1

\int \frac{csc ^{2} ( x )}{cot ^{7} ( x )} d x

f (x) = \frac{ln ( x )}{20 + x}

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