Integrate the following functions. ∫1x−√xdx.
∫1x−√xdx=∫1√x(√x−1)dx Let √x−1=t⇒12√x=dtdx⇒dx=2√xdt ∴∫1√x(√x−1)dx=∫1√xt2√xdt=∫2tdt=2.log|t|+C=2log|√x−1|+C
Integrate the following functions. ∫cos√x√xdx.
Integrate the following functions. ∫1(1+cotx)dx.
Integrate the following functions. ∫(1+logx)2xdx.
Integrate the following functions. ∫(x+1)(x+logx)2xdx.