Evaluate the following integrals. \({\displaystyle\displaystyle \displaystyle\int \frac{e^{\sqrt{x}+

Question

Evaluate the following integrals. ${\displaystyle\displaystyle \displaystyle\int \frac{e^{\sqrt{x}+3}}{\sqrt{x}} \mathrm{ d}x}$ ${\displaystyle\displaystyle \displaystyle\int \frac{e^{\ln x + 5}}{x} \mathrm{ d}x}$ ${\displaystyle\displaystyle \displaystyle\int \frac{1}{x(1 - \ln x)^5} \mathrm{ d}x}$ ${\displaystyle\displaystyle \displaystyle\int \frac{(3 + \ln x)^5}{x} \mathrm{ d}x}$ ${\displaystyle\displaystyle \displaystyle\int \frac{1}{\sqrt{x}(1 - \sqrt{x})}\mathrm{ d}x}$ ${\displaystyle\displaystyle \displaystyle\int \frac{1}{\sqrt{x}\sqrt{1 - \sqrt{x}}}\mathrm{ d}x}$

Accepted Answer

(a) $2e^{\sqrt{x}+3}+C$ (b) $xe^5+C$ (c) $\frac1{4(1-\ln x)^4}+C$ (d) $\frac16(3+\ln x)^6+C$ (e) $-2\ln|1-\sqrt{x}|+C$ (f) $-4\sqrt{1-\sqrt{x}}+C$

Reciprocal Function

Reciprocal Function

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