What is the integral of-sqrt(x)+1 ?

The integral of-sqrt(x)+1 is -2/3 x^{3/2}+x+C

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integral of-sqrt(x)+1

\int - x + 1 d x

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

Solution steps

\int - x + 1 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 1 d x

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

\int 1 d x = x

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

Add a constant to the solution

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

x \to 1 lim (a x^{2} + b x + 1)

d er i v a t i v e f (x) = - 2 t^{2} + 3 t - 6

\frac{d}{d x} (\frac{d y}{d x}) + y = 1

in v erse l a pl a ce \frac{3 s + 2}{s ^{2} + 2 s + 10}

roo t s 2 a x + b

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