MHT CET202015 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual
7^ 7^ 7^ x 7^ 7^ x 7^ x ~d x=
Options
- A7^ 7^ 7^ x ( 7)³+C
- B7^ 7^ x ( 7)² +C
- C7^ 7^ x ( 7) +C
- D7^ 7⁷ x ( 7)³ +C
Correct answer
D. 7^ 7⁷ x ( 7)³ +C
Step-by-step solution
Let I = 7^ 7^ 7^ x 7^ 7^ x 7^ x dx Let y=7^ 7^ 7^ x y=7^ 7^ x ( 7) Differentiating w.r.t. x, we get 1 y d y d x =( 7) d d x (7^ 7^ x ) Let z=7^ 7^ x z=7^ x 7 Differentiating w.r.t. x , we get aligned & 1 z d z d x =7^ x ( 7)² & d d x (7^ 7^ x )=7^ 7^ x 7^ x ( 7)² d y d x =7^ 7⁷ 7^ 7^ x 7^ x ( 7)³ I=& d d x (7^ 7^ 7^ x ) 1 ( 7)³ d x= 7^ 7^ x ( 7)³ +C aligned