₀^ 2 ^5 ( x 4 ) d x is equal to

Step-by-step solution

₀^ 2 ^5 ( x 4 ) d x= ₀^ 2 (1- ^2 x 4 ) (1- ^2 x 4 ) x 4 d x Put ( x 4 )=t aligned & - ( x 4 ) d x 4 =d t & ( x 4 ) d x=-4 d t & ₀^ 2 ^5 ( x 4 ) d x=-4 (1-t^2 ) (1-t^2 ) d t & =-4 [ (1+t^4-2 t^2 ) d t . & =-4 [t+ t^5 5 - 2 t^3 3 ] & =-4 [ ( x 4 )+ ^5 ( x 4 ) 5 - 2 ^3 ( x 4 ) 3 ]₀^ 2 aligned =-4 [(0+0-0)- (1+ 1 5 - 2 3 ) ]= 32 15