Indefinite Integration — JEE Main PYQs & Practice Questions

Indefinite Integration is a Mathematics chapter in the JEE Main syllabus. This page brings together 60 previous-year and practice questions on Indefinite Integration, organised into 4 topics: Standard Integrals, Integration by Substitution, Integration by Parts and Partial Fractions. Most questions come with a step-by-step solution you can work through free in PrepWiser.

Download Indefinite Integration JEE Main PYQs as a free PDF (with answer key)

Revise this chapter: Revision notes · Formula sheet

Chapter weightage: how many questions each chapter had per shift in the 2024–26 papers.

Standard Integrals

• The integral ∫ [(x/2)ˣ+(2/x)ˣ]ln (ex/2)dx is equal to :
• Let I(x)=∫ dx/(x-11)^(11/13)(x+15)^(15/13). If…
• If ∫ (x²+1)eˣ/(x+1)²dx=f(x)eˣ+C, where C is a constant, then d³f/dx³ at x = 1 is equal…
• If ∫ 1/(a²sin² x+b²cos² x) dx=1/12 tan⁻¹(3 tan x)+ constant, then the maximum value of a…
• Let f and g be the twice differentiable functions on ℝ such that f''(x)=g''(x)+6x…
• For α,β,γ,δ∈ ℕ, if ∫ ((x/e)²ˣ+(e/x)²ˣ)logₑ xdx=1/α(x/e)^(β x)-1/γ(e/x)^(δ x)+C , where…
• If ƒ'(x) = tan –1 (secx + tanx), -π/2<x<π/2, and ƒ(0) = 0, then ƒ(1) is equal to :
• The integral∫ (1-1/√3)(cos x-sin x)/(1+2/√3 sin 2x)dx is equal to
• The integral ∫ (x/(x sin x+cos x))²dx is equal to (where C is a constant of integration):

Integration by Substitution

• If ∫ dx/(x²+x+1)²=atan⁻¹((2x+1)/√3)+b((2x+1)/(x²+x+1))+C, x > 0 where C is the constant…
• Let f(t) = ∫₀ᵗ e^(x³)( x⁸/(x⁶ + 2x³ + 2)² )dx . If f(1) + f'(1) = α e - 1/6, then the…
• If ∫ (2x²+5x+9)/√(x²+x+1) dx=x√(x²+x+1)+α√(x²+x+1)+β logₑ|x+1/2+√(x²+x+1)|+C, where C is…
• The slope of the tangent to a curve C: y=y(x) at any point (x, y) on it is (2 e²ˣ-6…
• If ∫ √(sec 2x-1)dx=α logₑ|cos 2x+β+√(cos 2x(1+cos 1/βx))|+ constant, then β-α is equal…
• If ∫ (cos xdx)/sin³x(1+sin⁶x)^(2/3)=f(x)(1+sin⁶x)^(1/λ)+c where c is a constant of…
• If ∫ (cos θ)/(5+7 sin θ-2cos²θ)dθ = Alogₑ|B(θ)|+C, where C is a constant of integration…
• Let f(t)=∫ ((1-sin (logₑ t))/(1-cos (logₑ t)))dt,t>1. If f(e^(π/2))=-e^(π/2) and…
• If ∫ sin⁻¹(√(x/(1+x)))dx = A(x)tan⁻¹(√x) + B(x) + C, where C is a constant of…
• If ∫ (cos x-sin x)/√(8-sin 2x)dx=asin⁻¹((sin x+cos x)/b)+c, where c is a constant of…
• If ∫ (sin^(3/2) x+cos^(3/2) x)/√(sin³ x cos³ x sin (x-θ))dx=A√(cos θ tan x-sin θ)+B√(cos…
• Let f(x)=∫ dx/(3+4x²)√(4-3x²),|x|<2/√3. If f(0)=0 and f(1)=1/αβ tan⁻¹(α/β), α,β>0, then…
• If ∫ (sin x)^(-11/2)(cos x)^(-5/2)dx=-p₁/q₁(cot x)^(9/2)-p₂/q₂(cot x)^(5/2)-p₃/q₃(cot…
• If ∫ (1/x+1/x³)(²³√(3x⁻²⁴+x⁻²⁶))dx=-α/3(α+1)(3x^β+x^γ)^((α+1)/α)+C,x>0,(α,β,γ∈ Z), where…
• Let ∫ (2-tan x)/(3+tan x) dx=1/2(α x+logₑ|β sin x+γ cos x|)+C, where C is the constant…
• Let f(x)=∫ 2x/(x²+1)(x²+3)dx. If f(3)=1/2(logₑ5-logₑ6), then f(4) is equal to
• Let I(x)=∫ √((x+7)/x) dx and I(9)=12+7 logₑ 7. If I(1)=α+7 logₑ(1+2√2), then α⁴ is equal…
• The integral ∫ ((2x-1)cos √((2x-1)²+5))/√(4x²-4x+6)dx is equal to (where c is a constant…
• Let I(x)=∫ (x+1)/x(1+xeˣ)²dx,x>0. If limI(x)=0, then I(1) is equal to :
• Let I(x)=∫ 3dx/(4x+6)(√(4x²+8x+3)) and I(0)=√3/4+20. If I(1/2)=a√2/b+c, where a,b,c∈…

Integration by Parts

• For I(x)=∫ (sec² x-2022)/(sin²⁰²² x)dx, if I(π/4)=2¹⁰¹¹, then
• If ∫ eˣ((x sin⁻¹ x)/√(1-x²)+(sin⁻¹ x)/(1-x²)^(3/2)+x/(1-x²))dx=g(x)+C, where C is the…
• Let g:(0,∞ ) → R be a differentiable function such that ∫ ( x(cos x - sin x)/(eˣ + 1) +…
• Let I(x)=∫ x²(x sec² x+tan x)/(x tan x+1)²dx. If I(0)=0, then I(π/4) is equal to :
• If I(x)=∫ e^(sin²x)(cos x sin 2x-sin x)dx and I(0)=1, then I(π/3) is equal to :
• Let ∫ x³sin x dx=g(x)+C, where C is the constant of integration. If…
• If ∫ cosec⁵xdx=α cot xcosecx(cosec²x+3/2)+β logₑ|tan x/2|+C where α,β∈ ℝ and C is the…

Partial Fractions

• Let f(x)=∫ ((16x+24)/(x²+2x-15))dx. If f(4)=14 logₑ(3) and f(7)=logₑ(2^α· 3^β), α,β∈ ℕ…
• If ∫ (sin x)/(sin³x+cos³x)dx= αlogₑ|1+tan x|+βlogₑ|1-tan x+tan²x|+γtan⁻¹((2 tan…
• For k ∈ N, let 1/(α (α + 1)(α + 2).........(α + 20)) = Σ_(K = 0)²⁰ Aₖ/(α + k) , where α…
• Let f(x)=∫ dx/(x^(2/3)+2x^(1/2)), be such that f(0)=-26+24 logₑ(2). If f(1)=a+b logₑ(3)…
• If ∫ (2eˣ+3e⁻ˣ)/(4eˣ+7e⁻ˣ)dx=1/14(ux+vlogₑ(4eˣ+7e⁻ˣ))+C, where C is a constant of…

More Mathematics chapters

• Sets
• Relations & Functions (Basic)
• Trigonometric Ratios & Identities
• Trigonometric Equations
• Inverse Trigonometric Functions
• Properties of Triangles
• Complex Numbers
• Quadratic Equations & Polynomial Inequalities
• Sequences & Series
• Binomial Theorem
• Permutations & Combinations
• Mathematical Induction
• Statistics
• Probability — Basic
• Straight Lines
• Circles
• Parabola
• Ellipse
• Hyperbola
• Limits
• Continuity & Differentiability
• Differentiation
• Applications of Derivatives
• Definite Integration
• Area Under Curves
• Differential Equations
• Vectors
• Three Dimensional Geometry
• Matrices
• Determinants
• Functions (Advanced)
• Probability — Advanced

Frequently asked questions

How many Indefinite Integration questions are there for JEE Main?

PrepWiser has 60 Indefinite Integration questions for JEE Main, grouped into 4 topics such as Standard Integrals, Integration by Substitution and Integration by Parts.

Are these Indefinite Integration questions from previous-year JEE Main papers?

Yes — most are genuine previous-year questions from past JEE Main papers, and the rest are practice questions written to match the JEE Main pattern and difficulty.

Where can I see the answers and solutions to these Indefinite Integration questions?

Open any Indefinite Integration question in PrepWiser (it is free) to attempt it; most come with a step-by-step solution.