Question

integrate 1 - X into root x into DX

Answer 1

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Answer 2

Given:

• A function  $1- x \sqrt{x}$ is given.

To Find:

• Integrate the function $1- x \sqrt{x}$

Solution:

               $I = \int (1- x \sqrt{x}) dx$

               $I = \int (1- x \times x^{\frac{1}{2} }) dx$

              $I = \int (1- x^{\frac{3}{2} }) dx$

             $I = \int 1 dx- \int x^{\frac{3}{2} } dx$

             $I = x - \frac{x^{\frac{3}{2} +1}}{ \frac{3}{2} +1} + C$

             $I = x - \frac{2}{5} x^{ \frac{5}{2} } + C$

            $I = x - \frac{2}{5} x^2 \sqrt{x} } + C$

Thus,  

              $\int (1- x \sqrt{x}) dx =x - \frac{2}{5} x^2 \sqrt{x} } + C$