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

The integral of sqrt(x)-(x-2) is 2/3 x^{3/2}-(x^2)/2+2x+C

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integral of sqrt(x)-(x-2)

\int x - (x - 2) d x

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

Solution steps

\int x - (x - 2) d x

Simplify

= \int x - x + 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 d x - \int x d x + \int 2 d x

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

ln (w)

\frac{d}{d t} (a cos (t) + t^{2} sin (t))

g (t) = 3 t + 5 t + 9

(2 x + 8 y) d x + (8 x + 4 y) d y = 0

f (x) = \frac{x}{x ^{2} - 5}

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