` int (x) /(sqrt(1+x) )dx ` के लिए व्यंजक निकालें|

Explanation

मान लें ` 1+ x=y,` तो
` " " x= y-1 ` तथा ` (dy)/(dx) =1`
या ` " " dx= dy `
अतः `int (xdx)/(sqrt(1+ x))=int ((y-1))/sqrt(y)dy `
` " " = int [sqrt(y) -(1)/(sqrt(y) )] dy =int y^((1)/(2)) dy -int y^((1)/(2) ) dy`
` " " = (y^((3) /(2) ))/(3) -( y^((1)/(2)))/(1) =(2)/(3) y^((3)/(2)) -2y^((1)/(2))`
` " "= (2)/(3) (1+ x)^((3)/(2))-2 sqrt((1+x))*`