What is the integral of (x^2)/(x^3)+5 ?

The integral of (x^2)/(x^3)+5 is ln|x|+5x+C

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integral of (x^2)/(x^3)+5

\int \frac{x ^{2}}{x ^{3}} + 5 d x

ln ∣ x ∣ + 5 x + C

Solution steps

\int \frac{x ^{2}}{x ^{3}} + 5 d x

Cancel

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

= \int \frac{1}{x} + 5 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}{x} d x + \int 5 d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 5 d x = 5 x

= ln ∣ x ∣ + 5 x

Add a constant to the solution

= ln ∣ x ∣ + 5 x + C

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k = 1 \sum \infty \frac{k ^{3}}{5 ^{k}}

\int \frac{7 sin ( x ) + 2 sec ( x )}{tan ( x )} d x

What is the integral of (x^2)/(x^3)+5 ?
The integral of (x^2)/(x^3)+5 is ln|x|+5x+C