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Integration by substitution, by parts and by partial fractions Previous Year Questions for JEE

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Goodmarks offers 5+ JEE-style PYQs for Integration by substitution, by parts and by partial fractions with detailed solutions. While official past papers rotate yearly, our bank covers the same concepts, difficulty, and question formats tested in JEE Mathematics.

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Syllabus context

Part of Integral Calculus in JEE Main Mathematics.

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Q1MathsUnit 8: Integral Calculus
x+2x3−x=\frac{\boldsymbol{x}+\mathbf{2}}{\boldsymbol{x}^{\boldsymbol{3}}-\boldsymbol{x}}=
Q2MathsUnit 8: Integral Calculus
∫cos⁡x−cos⁡3x1−cos⁡3xdx=\int \sqrt{\frac{\cos x-\cos ^{3} x}{1-\cos ^{3} x}} d x=
Q3MathsUnit 8: Integral Calculus
∫(tan⁡10x+tan⁡12x)dx=\int\left(\tan ^{10} x+\tan ^{12} x\right) d x=
Q4MathsUnit 8: Integral Calculus
∫(2x+1)(x2+4x+1)32dx\int \frac{(\mathbf{2} \boldsymbol{x}+\mathbf{1})}{\left(\boldsymbol{x}^{2}+\mathbf{4} \boldsymbol{x}+\mathbf{1}\right)^{\frac{\mathbf{3}}{\mathbf{2}}}} \boldsymbol{d} \boldsymbol{x}
Q5MathsUnit 8: Integral Calculus
∫(sin⁡x)99(cos⁡x)−101dx=−…−C\int(\sin x)^{99}(\cos x)^{-101} d x=_{-} \ldots-C_{ }

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Why practise PYQs for Integration by substitution, by parts and by partial fractions?

PYQs reveal recurring concepts, common traps, and the difficulty level JEE expects. Solving them builds exam temperament and time management.

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Our bank includes exam-style MCQs aligned with JEE Main Mathematics syllabus for Integration by substitution, by parts and by partial fractions, covering the same topics as previous year papers.

How should I use PYQs for Integral Calculus?

Solve timed sets, review every explanation, note weak subtopics, then revisit with focused practice on Goodmarks.

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