What is the integral of f(x) = 1 + x2 + x4 with respect to x2?

$\rm x^2 + \frac{x^4}{2}+\frac{x^6}{3}+C$

$\rm x + \frac{x^3}{3}+\frac{x^5}{5}+C$

$\rm \frac{x^3}{3}+\frac{x^5}{5}+C$

$\rm x^2 + \frac{x^4}{4}+\frac{x^6}{6}+C$

What is $\int \frac{dx}{10^{x}+10^{-x}}$ equal to?

$\frac{1}{\ln 10}\tan^{-1}(10^{x})+c$

Indefinite Integration — NDA Previous Year Questions

21 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 21
Years covered: 2021–2025
Avg / year: ~5
Subject: Mathematics

How many NDA questions come from Indefinite Integration?

Indefinite Integration has contributed 21 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 5 questions a year. That count is measured from EByAi’s bank of 15,695 NDA questions, not estimated from a syllabus. Every one of the 21 questions carries a written, step-by-step solution, and each is tagged to Indefinite Integration within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Indefinite Integration questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 21 Indefinite Integration questions (with full written solutions) are available in practice.

Question 1 · NDA 2021
What is the integral of f(x) = 1 + x2 + x4 with respect to x2?
1. (A) $x + \frac{x ^{3}}{3} + \frac{x ^{5}}{5} + C$
2. (B) $\frac{x ^{3}}{3} + \frac{x ^{5}}{5} + C$
3. (C) $x^{2} + \frac{x ^{4}}{4} + \frac{x ^{6}}{6} + C$
4. (D) $x^{2} + \frac{x ^{4}}{2} + \frac{x ^{6}}{3} + C$
Show answerAnswer
$Answer: (D) x^{2} + \frac{x ^{4}}{2} + \frac{x ^{6}}{3} + C$
Question 2 · NDA 2025
What is $\int \frac{d x}{1 0 ^{x} + 1 0 ^{- x}}$ equal to?
1. (A) $tan^{- 1} (1 0^{x}) + c$
2. (B) $(ln 10) tan^{- 1} (1 0^{x}) + c$
3. (C) $\frac{1}{l n 10} tan^{- 1} (1 0^{x}) + c$
4. (D) $ln (1 0^{x} + 1 0^{- x}) + c$
Show answerAnswer
$Answer: (C) \frac{1}{l n 10} tan^{- 1} (1 0^{x}) + c$
Question 3 · NDA 2025
$W ha t i s \int y d x e q u a l t o ?$

where c is the constant of integration.
1. (A) $-tan(x/2)+c$
2. (B) $-cot(x/2)+c$
3. (C) $tan(x/2)+c$
4. (D) $cot(x/2)+c$
Show answerAnswer
$Answer: (B) -cot(x/2)+c$
Question 4 · NDA 2025
Consider the following:

I. $\frac{d u}{d x} = - v$

II. $\frac{d v}{d x} = - u$

Which of the above is/are correct?
1. (A) $I only$
2. (B) $II only$
3. (C) $Both I and II$
4. (D) $Neither I nor II$
Show answerAnswer
$Answer: (D) Neither I nor II$
Question 5 · NDA 2022
What is $\int (sin x)^{- 1/2} (cos x)^{- 3/2} d x$ equal to?
1. (A) $tan x + c$
2. (B) $2 tan x + c$
3. (C) $cot x + c$
4. (D) $2 tan x + c$
Show answerAnswer
$Answer: (B) 2 tan x + c$

Indefinite Integration questions by year

Year	Questions	Share of chapter questions
2025	4
2024	6
2022	5
2021	6

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FAQs

How many NDA questions have been asked from Indefinite Integration?

EByAi's bank holds 21 real NDA questions from Indefinite Integration, asked between 2021 and 2025 — about 5 per year on average. Every count is measured from actual papers, not estimated.

Is Indefinite Integration important for NDA?

21 questions over 4 papers make Indefinite Integration a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Indefinite Integration PYQs online for free?

Yes. EByAi lets you solve NDA past-year questions in the browser with written solutions — free daily practice, no card needed.

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