evaluate the following indefinite integral.\n\n$$ int \frac { 7 } { sqrt { x } } d x $$\n$$ int \frac { 7 }…

Explanation:

Step1: Rewrite the integrand

We know that (\frac{1}{\sqrt{x}}=x^{-\frac{1}{2}}). So, (\int\frac{7}{\sqrt{x}}dx = 7\int x^{-\frac{1}{2}}dx)

Step2: Apply the power - rule for integration

The power - rule for integration is (\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C) ((n\neq - 1)). For (n=-\frac{1}{2}), we have: (7\int x^{-\frac{1}{2}}dx=7\times\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C) (=7\times\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C)

Step3: Simplify the expression

(7\times\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C=14\sqrt{x}+C)

Answer:

(14\sqrt{x}+C)