^2 x ( x+ x)^ 9 / 2 d x equals

Step-by-step solution

Let I= ^2 x ( x+ x)^ 9 / 2 d x Put x+ x=t Then, x- x= 1 t and x( x+ x) d x=d t x d x= 1 t d t Also, x= 1 2 (t+ 1 t ) I= 1 2 1 t (t+ 1 t ) t^ 9 / 2 d t aligned & I= 1 2 1 t^ 9 / 2 + 1 t^ 13 / 2 d t & I=- 1 7 t^ 7 / 2 - 1 11 t^ 11 / 2 +K & I=- 1 t^ 11 / 2 t^2 7 + 1 11 +K & I=- 1 ( x+ x)^ 11 / 2 & 1 11 + 1 7 ( x+ x)^2 +K aligned