If [3] x 1+ [3] x^4 ^ 1 / 7 d x=A (1+ [3] x^4 )^B+c , then value of A B is equal to

Step-by-step solution

[3] x 1+ [3] x^4 ^ 1 7 d x=A (1+ [3] x^4 )^B+c Let us assume I= [3] x (1+ [3] x^4 )^ 1 7 = x^ 1 3 (1+x^ 4 3 )^ 1 7 d x aligned & Let 1+x^ 4 3 =t & aligned 4 3 x^ 4 3 -1 d x & =d t 4 3 x^ 1 3 d x=d t x^ 1 3 d x & = 3 4 d t I & = (t)^ 1 7 3 4 d t= 3 4 (t)^ 1 7 d t & = 3 4 [ (t)^ 1 7 +1 1 7 +1 ]+c= 3 4 (1+x^ 4 / 3 )^ 8 7 8 7 +c & = 21 32 (1+ [3] x^4 )^ 8 7 +c aligned aligned aligned & A= 21 32 and B= 8 7 & A B= 21 32 8 7 = 3 4 aligned