Find the following integral. \int \frac{3-x}{\sqrt{x}}dx

Question

Find the following integral.

\int \frac{3 - x}{\sqrt{x}} d x

Answer 1

Given that

\int \frac{3 - x}{\sqrt{x}} d x

= 3 \int \frac{1}{\sqrt{x}} d x - \int \sqrt{x} d x

= 3 [\frac{x^{\frac{- 1}{2} + 1}}{\frac{- 1}{2} + 1}] - [\frac{x^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}] + C

= 3 (2 \sqrt{x}) - \frac{2}{3} \cdot x^{\frac{3}{2}} + C

∴ \int \frac{3 - x}{\sqrt{x}} d x = 6 \sqrt{x} - \frac{2}{3} \cdot x^{\frac{3}{2}} + C

Expert Answer