What is the integral of sqrt(x)-2/(x^5)+7/x ?

The integral of sqrt(x)-2/(x^5)+7/x is 2/3 x^{3/2}+1/(2x^4)+7ln|x|+C

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integral of sqrt(x)-2/(x^5)+7/x

\int x - \frac{2}{x ^{5}} + \frac{7}{x} d x

\frac{2}{3} x^{\frac{3}{2}} + \frac{1}{2 x ^{4}} + 7 ln ∣ x ∣ + C

Solution steps

\int x - \frac{2}{x ^{5}} + \frac{7}{x} 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{2}{x ^{5}} d x + \int \frac{7}{x} d x

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

\int \frac{2}{x ^{5}} d x = - \frac{1}{2 x ^{4}}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= \frac{2}{3} x^{\frac{3}{2}} - (- \frac{1}{2 x ^{4}}) + 7 ln ∣ x ∣

Simplify

= \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{2 x ^{4}} + 7 ln ∣ x ∣

Add a constant to the solution

= \frac{2}{3} x^{\frac{3}{2}} + \frac{1}{2 x ^{4}} + 7 ln ∣ x ∣ + C

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What is the integral of sqrt(x)-2/(x^5)+7/x ?
The integral of sqrt(x)-2/(x^5)+7/x is 2/3 x^{3/2}+1/(2x^4)+7ln|x|+C