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JEE Main20248 Apr 2024Evening ShiftMathematicsIndefinite IntegrationActual

If 1 [5] (x-1)^4(x+3)^6 ~d x= A ( x-1 x+3 )^B+ C , where C is the constant of integration, then the value of + +20 AB is__________

Correct answer

0

Step-by-step solution

aligned & 1 [5] (x-1)^4(x+3)^6 d x=A ( x-1 x+3 )^B+C & I= 1 (x-1)^ 4 / 5 (x+3)^ 6 / 5 d x & I= 1 ( x-1 x+3 )^ 4 / 5 (x+3)^2 d x & ( x-1 x+3 )=t 4 (x+3)^2 d x=d t t^ -4 / 5+1 & I= 1 4 1 t^ 4 / 5 d t= 1 4 t^ 1 / 5 1 / 5 +c & I= 5 4 ( x-1 x+3 )^ 1 / 5 +C & A= 5 4 = =1 B= 1 5 & + +20 A B=2+20 5 4 1 5 =7 aligned

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