What is the integral of x-(-\sqrt{)x ?

The integral of x-(-\sqrt{)x is (x^2)/2+(sqrt(d)x^2)/2+C

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integral of x-(-\sqrt{)x

\int x - (- d) x d x

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

Solution steps

\int x - (- d) 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 d x - \int (- d) x d x

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

\int (- d) x d x = - \frac{d x ^{2}}{2}

= \frac{x ^{2}}{2} - (- \frac{d x ^{2}}{2})

Simplify

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

Add a constant to the solution

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

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What is the integral of x-(-\sqrt{)x ?
The integral of x-(-\sqrt{)x is (x^2)/2+(sqrt(d)x^2)/2+C