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Popular >

integral of x^{-5}+x^{1/2}

Solution

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

Solution

- \frac{1}{4 x ^{4}} + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

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

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

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

= - \frac{1}{4 x ^{4}} + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{1}{4 x ^{4}} + \frac{2}{3} x^{\frac{3}{2}} + C

Popular Examples

derivative of (-x^2+25^2)

\frac{d}{d x} ((- x^{2} + 25)^{2})

integral of 7/(x^3-125)

\int \frac{7}{x ^{3} - 125} d x

(\partial)/(\partial y)(sin^2(x-3y))

\frac{\partial}{\partial y} (sin^{2} (x - 3 y))

derivative of scos(x)

\frac{d}{d x} (s cos (x))

sum from n=2 to infinity of 1/(n^4)

n = 2 \sum \infty \frac{1}{n ^{4}}

Frequently Asked Questions (FAQ)

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