Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2018MathematicsIndefinite IntegrationActual

Let P x = ∫ d x e x + 8 e - x + 4 e - 3 x , Q x = ∫ d x e 3 x + 8 e x + 4 e - x and R x = P x - 2 Q x . If R x = 1 2 A B + 2 e - x C + K , then the value of A , B , C is

Options

  1. Atan - 1 , 2 , e x
  2. Btan - 1 , e x , 2
  3. Ctan - 1 , 1 2 , 1 e x
  4. Dtan - 1 , 1 e x , 1 2

Correct answer

B. tan - 1 , e x , 2

Step-by-step solution

We have, R x = ∫ d x e x + 8 e - x + 4 e - 3 x - 2 ∫ d x e 3 x + 8 e x + 4 e - x ⇒ R x = ∫ e x e 2 x - 2 e 4 x + 8 e 2 x + 4 d x we get R t = ∫ t 2 - 2 d t t 4 + 8 t 2 + 4 = ∫ 1 - 2 t - 2 d t t + 2 t - 1 2 + 4 = 1 2 tan - 1 t + 2 t - 1 2 + K ⇒ R x = 1 2 tan - 1 e x + 2 e - x 2 + K Hence, A , B , C = tan - 1 , e x , 2 ∴ Option (b) is correct.

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

The value of e^ ( - ) d is 2024⁻¹ x dx is equal to 2023Value of d x x(a-x) is 2023If e ^ x (1+ x ) dx 1+ x = e ^ x f ( x )+ C , then f ( x ) is equal to 2023x+3 (x+4)^2 e^x d x is equal to 2023The value of 1 [(x-1)^3(x+2)^5 ]^ 1 4 d x , is 2022Let f(x)= x^2 d x (1+x^2 ) (1+ .1+x^2 ) . and f(0)=0 , then the value of f(1) be 2022If x (x- ) d x = A x+ B (x- )+ C , then value of (A, B) is 2021 Full Indefinite Integration list All BITSAT PYQs