ज्ञात करें `int(5x+3)sqrt(2x-1)dx`

Explanation

यहां `p(x)=5x+3` तथा `sqrt(2x-1), (ax+b)^n` के रूप का है |
माना की `z=2x-1` तो `dz=2dx :. dd = (dz)/(2)`
पुनः `int(5x+3)srt(2x-1)dx=int[5((z+1)/2)+3]sqrtz(dx)/2`
`=5/4intz^(3/4)dz+11/4intsqrtz dz`
`=5/4*z^(5/4)/(5/2)+11/4*z^(3/2)/(3/2)+c=1/2z^(5/2)+11/5z^(3/2)+c`
`=z^(3/2)/(2)(z+11/2)+c=z^(3/2)/2((3z+11)/3)+c`
`=((2x-1)^(3/2))/6*[3(2x-1)+11]+c`
`=((2x-1)^(3/2))/6*(6x+8)+c=((2x-1)^(3/2)*(3x+4))/3+c`