MHT CET202012 Oct 2020Evening ShiftMathematicsIndefinite IntegrationActual
5^ x 5(-2 x)-5^ (2 x) d x=
Options
- A⁻¹ (5^ 2 x )+c
- B⁻¹ (5^ 2 x ) 25 +c
- C⁻¹ (5^ x )+c
- D⁻¹ (5^ 2 x ) 25+c
Correct answer
B. ⁻¹ (5^ 2 x ) 25 +c
Step-by-step solution
Let aligned I &= 5^ x (5^ 2 x )⁻¹-5^ 2 x d x &= 5^ x ( 1 5^ 2 x )-5^ 2 x d x= 5^ x 5^ x 1- (5^ 2 x ) d x aligned Put 5^ 2 x = t (2 5) 5^ 2 x dx = dt 5^ x 5^ x dx = dt 25 aligned I &= 1 1- t ² dt ( 25) = 1 25 dt 1- t ² dt &= 1 25 ⁻¹ t + c = 1 25 ⁻¹ (5^ 2 x )+ c aligned