Question

Current Attempt in ProgressFind the indefinite integral. Check your answer by differentiation.XJdx =+C√x² +5

Answer 1

We solve the inequality

`\begin{gathered} Let\text{ }I=\int(x)/(√(x^2+5))dx \\ \\ Let\text{ }u=x^2+5 \\ \\ du=2xdx \\ \\ I=\int(x)/(√(x^2+5))dx=\int(1)/(√(u))*(1)/(2)du \\ \\ I=(1)/(2)\int u^{-(1)/(2)}du \\ \\ I=(1)/(2)*\frac{u^{(1)/(2)}}{(1)/(2)} \\ \\ I=u^{(1)/(2)} \\ \\ I=√(x^2+5)+C \end{gathered}`