Mathematics - Indefinite Integration Question with Solution | TestHub

$\int \frac{(2x-1)\cos \sqrt{(2x-1{)}^2+5}}{\sqrt{(2x-1{)}^2+5}}dx$

$(2x-1{)}^2+5=t^2$

$2\left(2x-1\right) 2dx=2 tdt$

$2\sqrt{t^2-5}dx=tdt$

So $\int \frac{\sqrt{t^2-5}\cos t}{2\sqrt{t^2-5}}dt=\frac{1}{2}\sin t+c$

$=\frac{1}{2}\sin \sqrt{(2x-1{)}^2+5}+c$