MHT CET202415 May 2024Morning ShiftMathematicsIndefinite IntegrationActual
The value of d x 5+4 x is equal to
Options
- A2 5 ⁻¹ ( 5 x 2 +4 3 )+ c , (where c is a constant of integration) .
- B2 3 ⁻¹ ( 5 x 2 +4 3 )+ c , (where c is a constant of integration)
- C2 5 ( 5 x 2 +7 5 x 2 +1 )+ c , (where c is a constant of integration)
- D2 3 ( 5 x 2 +7 5 x 2 +1 )+ c , (where c is a constant of integration)
Correct answer
B. 2 3 ⁻¹ ( 5 x 2 +4 3 )+ c , (where c is a constant of integration)
Step-by-step solution
array ll & Let I= d x 5+4 x & Put ( x 2 )= t & x=2 ⁻¹ t & d x= 2 dt 1+ t ^2 and x= 2 t 1+ t ^2 & I = 2 dt 5+4 ( 2 t 1+ t ^2 ) array aligned & =2 d t 5+5 t^2+8 t & = 2 5 d t t^2+ 8 t 5 +1 & = 2 5 d t t^2+ 8 5 t+1- 16 25 + 16 25 & = 2 5 d t (t+ 4 5 )^2+ ( 3 5 )^2 aligned aligned & = 2 5 1 3 5 ⁻¹ ( t + 4 5 3 5 )+ c & = 2 3 ⁻¹ [ 5 ( x 2 )+4 3 ]+ c aligned