AP EAMCET2004MathematicsIndefinite Integration
d x (x+100) x+99 =f(x)+c f(x)
Options
- A2(x+100)^ 1 / 2
- B3(x+100)^ 1 / 2
- C2 ⁻¹( x+99 )
- D2 ⁻¹( x+100 )
Correct answer
C. 2 ⁻¹( x+99 )
Step-by-step solution
Let aligned I & = d x (x+100) x+99 & = d x .( x+99 )^2+1 ) x+99 aligned Put x+99 =t 1 x+99 d x=2 d t aligned I & = 2 d t t^2+1 =2 ⁻¹ t+c & =2 ⁻¹ x+99 +c aligned From Eqs. (i) gathered 2 ⁻¹ x+99 +c=f(x)+c f(x)=2 ⁻¹ x+99 gathered