AP EAMCET202418 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
1 x^5 [5] x^5+1 d x=
Options
- A4 [5] x^5+1 +c
- B4 x^4 (x^5+1 )^ 4 5 +c
- C- (x^5+1 )^ 4 5 4 x^4 +c
- D- (x^5+1 )^ 4 5 4 x^5 +c
Correct answer
C. - (x^5+1 )^ 4 5 4 x^4 +c
Step-by-step solution
Let, I = 1 x^5 [5] x^5+1 d x= 1 1^ 1 5 d xx^6 (1+ 1 x^5 )^ 5 Let 1+ 1 x^5 =t 1 x^6 d x=- 1 5 d t Now, I = -1 5 1 t^ 1 5 d t=- 1 5 t^ -1 5 d t= -1 5 t^ 4 5 4 5 + C = -1 4 t^ 4 5 + C =- 1 4 (1+ 1 x^5 )^ 4 5 + C = - (1+x^5 )^5 4 x^4 + C