What is the integral of x^4+1/(2sqrt(x)) ?

The integral of x^4+1/(2sqrt(x)) is (x^5)/5+sqrt(x)+C

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integral of x^4+1/(2sqrt(x))

\int x^{4} + \frac{1}{2 x} d x

\frac{x ^{5}}{5} + x + C

Solution steps

\int x^{4} + \frac{1}{2 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^{4} d x + \int \frac{1}{2 x} d x

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

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

= \frac{x ^{5}}{5} + x

Add a constant to the solution

= \frac{x ^{5}}{5} + x + C

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What is the integral of x^4+1/(2sqrt(x)) ?
The integral of x^4+1/(2sqrt(x)) is (x^5)/5+sqrt(x)+C