Question

Evaluate the integrals. int e^{lnsqrt x}dx

Integrals
ANSWERED
asked 2020-10-18
Evaluate the integrals.
\(\int e^{ln\sqrt x}dx\)

Answers (1)

2020-10-19
\(\text{Given,}\int e^{\ln\sqrt x}dx\)
\(\text{On simplification, we get}\)
\(\int e^{\ln\sqrt x}dx=\int\sqrt xdx\ \ \ [\because e^{\ln x}]\)
\(\text{Now on integrating, we get}\)
\(\int \sqrt xdx=\int x^{1/2}dx\)
\(=\frac{x^{3/2}}{3/2}+C\ \ [\because\int x^n dx=\frac{x^{n+1}}{n+1}]\)
\(=\frac{2}{3}x^{3/2}+C\)
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