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

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

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

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

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

Solution steps

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

Expand

\frac{x ^{4} + 4}{x ^{3}} : x + \frac{4}{x ^{3}}

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

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

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

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

Add a constant to the solution

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

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 2 t}

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

(sin (x) sin (2 x) sin (3 x))^{^{'}}

y = e^{x} sin (2 x)

x \to 0 + lim (x ln (sin (x)))

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