What is the integral of xsqrt(2)-1/(2sqrt(x)) ?

The integral of xsqrt(2)-1/(2sqrt(x)) is (x^2)/(sqrt(2))-sqrt(x)+C

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integral of xsqrt(2)-1/(2sqrt(x))

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

\frac{x ^{2}}{2} - x + C

Solution steps

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

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

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

= \frac{x ^{2}}{2} - x

Add a constant to the solution

= \frac{x ^{2}}{2} - x + C

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