Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2017MathematicsIndefinite IntegrationActual

What is ( x ^ e -1 + e ^ x -1 ) dx x ^ e + e ^ x equal to?

Options

  1. Ax ^2 2 + c
  2. BIn (x+e)+c
  3. CIn ( x ^ e + e ^ x )+ c
  4. D1 e In ( x ^ e + e ^ x )+ c

Correct answer

D. 1 e In ( x ^ e + e ^ x )+ c

Step-by-step solution

aligned & ( x ^ e -1 + e ^ x -1 ) dx x ^ e + e ^ x & Put x ^ e + e ^ x = t ex e ^ e -1 + e ^ x = dt dx & ( ex e ^ e -1 + e ^ x ) dx = dt & ( x ^ e -1 + e ^ x -1 ) dx x ^ e + e ^ x = 1 e e x ^ e -1 + e ^ x x ^ e + e ^ x dx & = 1 e dt t = 1 e t + c & = 1 e ( x ^ e + e ^ x )+ c aligned

Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

Passage: Let ,d (2+ )(3+4 ) =A |2+ |+B |3+4 | . Question: What is the value of A ? 2026Passage: Let ,d (2+ )(3+4 ) =A |2+ |+B |3+4 | . Question: What is the value of B ? 2026What is dx 10^x + 10^ -x equal to? 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)⁻¹ , where x 2n and n is an integer. What is y , dx equal to? 2025For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . Consider the following: I. du dx = -v II. dv dx = -u Which of the above is/are correct? 2025For the following two (02) items: Let u = e^x x , dx and v = e^x x , dx . What is u + v equal to? 2025Let d x x+1 - x-1 = (x+1)^ 3 2 + (x-1)^ 3 2 +c What is the value of ? 2024Paragraph: Let 2 x^2-1 x^2+1 d x= U (x) V (x)-3 U (x)+ V (x) +c Question: What is U (x) V (x) equal to? 2024 Full Indefinite Integration list All NDA PYQs