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

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

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

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

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

Solution steps

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

\frac{1 - x}{1 - x} = x + 1

= \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 + (- \infty) + lim (- x^{2})

\int_{0}^{1} \frac{4}{x ^{2}} d x

x \to 0 + lim (x^{- \frac{4}{l n ( x )}})

x \to 0 - lim (\frac{- 1}{x})

y = lo g_{5} (5 x + 4)

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