What is the integral of 1-x^{1/2} ?

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

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integral of 1-x^{1/2}

integral

1 - x^{\frac{1}{2}}

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

Solution steps

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

\int 1 d x = x

\int x^{\frac{1}{2}} d x = \frac{2}{3} x^{\frac{3}{2}}

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

Add a constant to the solution

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

\frac{1}{( 1 + x ^{2} )}

\frac{x ( 1 + 3 x ^{2} ) ^{5}}{2}

\frac{2}{t ^{3}}

\frac{x}{sin ^{2} ( x ^{2} )}

\frac{x}{16}

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