The integral ² x ( x+ x)^ 9 2 d x equals (for some arbitrary constant K )

Step-by-step solution

array l I= ² x ( x+ x)^ 9 / 2 d x Let x+ x=t x- x= 1 t x= 1 2 (t+ 1 t ) and x( x+ x) d x=d t x d x= d t t I= 1 2 (t+ 1 t ) d t t^ 9 / 2 t = 1 2 (t^ -9 / 2 +t^ -13 / 2 ) d t = -1 7 t^ -7 / 2 - 1 11 t^ -1 / 2 +K =- 1 7 t^ 7 / 2 - 1 11 t^ 11 / 2 +K=- 1 t^ 11 / 2 ( 1 11 + t² 7 )+K = -1 ( x+ x)^ 11 / 2 1 11 + 1 7 ( x+ x)² +K array