Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Indefinite Integration

NDA 2010 · Mathematics · Indefinite Integration

What is ∫ (x^4+1)/(x^2+1) d x equal to? where c is a constant of...

What is ∫x4+1x2+1dx\int \frac{x^4+1}{x^2+1} d x equal to? where cc is a constant of integration.

Options

  1. Ax33−x+4tan⁡−1x+c\frac{x^3}{3}-x+4 \tan ^{-1} x+c
  2. Bx33+x+4tan⁡−1x+c\frac{x^3}{3}+x+4 \tan ^{-1} x+c
  3. Cx33−x+2tan⁡−1x+c\frac{x^3}{3}-x+2 \tan ^{-1} x+c
  4. Dx33−x−4tan⁡−1x+c\frac{x^3}{3}-x-4 \tan ^{-1} x+c

Correct answer

C. x33−x+2tan⁡−1x+c\frac{x^3}{3}-x+2 \tan ^{-1} x+c

Step-by-step solution

The correct answer is option (C).
Practice Indefinite Integration on Quantrex Academy →

More from Indefinite Integration

Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value… NDA 2026Passage: Let ∫( θ\,dθ)/((2+ θ)(3+4 θ))=A |2+ θ|+B |3+4 θ| . Question: What is the value… NDA 2026What is ∫ dx 10^x + 10^ -x equal to? NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . Consider… NDA 2025For the following two (02) items: Let u = ∫ e^x x\, dx and v = ∫ e^x x\, dx . What is u +… NDA 2025Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of β ? NDA 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)… NDA 2024Paragraph: Let 2 ∫ x^2-1 x^2+1 d x=U(x) V(x)-3 \ U(x)+V(x)\ +c Question: What is… NDA 2024Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of… NDA 2024Given that ∫ (3 x+4 x)/(2 x+5 x) d x=(α x)/(29)+(β)/(29) |2 x+5 x|+c What is the value of… NDA 2024Let ∫ d x x+1 - x-1 =α(x+1)^ (3)/(2) +β(x-1)^ (3)/(2) +c What is the value of α ? NDA 2024Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further… NDA 2023Paragraph: Let f(x)=P e^x+Q e^ 2 x +R e^ 3 x , where P, Q, R are real numbers. Further… NDA 2023What is ∫(x^x)^2(1+ x) d x equal to? NDA 2022What is ∫ e^ x (1+ x+x x) d x equal to? NDA 2022 Full Indefinite Integration list Indefinite Integration JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs