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Important Questions: Integration by substitution, by parts and by partial fractions for JEE

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The most important Integration by substitution, by parts and by partial fractions questions for JEE cover conceptual traps, standard results, and numerical patterns from Integration by substitution, by parts and by partial fractions. Goodmarks provides 5+ high-yield MCQs with full solutions.

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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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What makes a Integration by substitution, by parts and by partial fractions question "important" for JEE?

Important questions test core concepts that appear frequently across JEE Main and Advanced papers — definitions, standard formulas, and classic problem types.

Which subtopics in Integral Calculus are high-weightage?

Key areas include Integration by substitution, by parts and by partial fractions. Prioritise these before moving to edge cases.

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Revise 30–50 important MCQs per unit in the last month before JEE. Focus on questions you got wrong at least once.

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