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Popular >

integral of (x^7)/2-1/(x^5)

Solution

\int \frac{x ^{7}}{2} - \frac{1}{x ^{5}} d x

Solution

\frac{x ^{8}}{16} + \frac{1}{4 x ^{4}} + C

Solution steps

\int \frac{x ^{7}}{2} - \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{x ^{7}}{2} d x - \int \frac{1}{x ^{5}} d x

\int \frac{x ^{7}}{2} d x = \frac{x ^{8}}{16}

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

= \frac{x ^{8}}{16} - (- \frac{1}{4 x ^{4}})

Simplify

= \frac{x ^{8}}{16} + \frac{1}{4 x ^{4}}

Add a constant to the solution

= \frac{x ^{8}}{16} + \frac{1}{4 x ^{4}} + C

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Frequently Asked Questions (FAQ)

What is the integral of (x^7)/2-1/(x^5) ?
The integral of (x^7)/2-1/(x^5) is (x^8)/(16)+1/(4x^4)+C