What is the integral of (10)/(x^4)+2/(x^{3/4)}+5 ?

The integral of (10)/(x^4)+2/(x^{3/4)}+5 is -(10)/(3x^3)+8x^{1/4}+5x+C

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integral of (10)/(x^4)+2/(x^{3/4)}+5

\int \frac{10}{x ^{4}} + \frac{2}{x ^{\frac{3}{4}}} + 5 d x

- \frac{10}{3 x ^{3}} + 8 x^{\frac{1}{4}} + 5 x + C

Solution steps

\int \frac{10}{x ^{4}} + \frac{2}{x ^{\frac{3}{4}}} + 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{10}{x ^{4}} d x + \int \frac{2}{x ^{\frac{3}{4}}} d x + \int 5 d x

\int \frac{10}{x ^{4}} d x = - \frac{10}{3 x ^{3}}

\int \frac{2}{x ^{\frac{3}{4}}} d x = 8 x^{\frac{1}{4}}

\int 5 d x = 5 x

= - \frac{10}{3 x ^{3}} + 8 x^{\frac{1}{4}} + 5 x

Add a constant to the solution

= - \frac{10}{3 x ^{3}} + 8 x^{\frac{1}{4}} + 5 x + C

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What is the integral of (10)/(x^4)+2/(x^{3/4)}+5 ?
The integral of (10)/(x^4)+2/(x^{3/4)}+5 is -(10)/(3x^3)+8x^{1/4}+5x+C