Calculus help please! Click the link to see the integral. \int\limits { (cosx)/( √(sinx) ) } \, dx

Question

Calculus help please! Click the link to see the integral.


`\int\limits { (cosx)/( √(sinx) ) } \, dx`

Answer 1

Let
`u=\sin x`, then
`\mathrm du=\cos x\,\mathrm dx`. Now


`\displaystyle\int(\cos x)/(√(\sin x))\,\mathrm dx=\int(\mathrm du)/(\sqrt u)=\int u^(-1/2)\,\mathrm du`

The power rule for integration gives


`\displaystyle\int u^(-1/2)\,\mathrm du=2u^(1/2)+C=2√(\sin x)+C`