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Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions Short Tricks for JEE

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Quick answer

Short tricks for Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions work only with strong fundamentals. Apply the tips below in timed sets and review every explanation.

Use these Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions shortcuts to save time in JEE Mathematics papers — then validate speed with 4+ MCQs on Goodmarks.

Short tricks for speed

  • Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions focus drill

    Solve 15 mixed MCQs for Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions, review every explanation, and note formulas you hesitated on.

  • Calculus substitution scan

    Spot standard forms (sin²x, 1/(a²+x²), e^ax) before integrating — JEE rewards pattern recognition.

  • Graph sketch shortcut

    For coordinate geometry, mark intercepts and asymptotes first; many MCQs need only qualitative graph features.

Syllabus context

Part of Integral Calculus in JEE Main Mathematics.

Free sample questions

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Q1MathsUnit 8: Integral Calculus
∫(e5log⁡x−e4log⁡xe3log⁡x−e2log⁡x)dx=\int\left(\frac{e^{5 \log x}-e^{4 \log x}}{e^{3 \log x}-e^{2 \log x}}\right) d x=
Q2MathsUnit 8: Integral Calculus
STATEMENT - 1: The volume of largest sphere that can be carved out from cube of side a cm is 16πa3\frac{1}{6} \pi a^{3} STATEMENT - 2: Volume of sphere is 43πr3\frac{4}{3} \pi r^{3} and for largest sphere to carved from cube radius of sphere == side of cube
Q3MathsUnit 8: Integral Calculus
A hollow spherical shell is made of metal of density 4.8g/cm3.4.8 \mathrm{g} / \mathrm{cm}^{3} . If its internal and external radii are 10cm10 \mathrm{cm} and 12cm12 \mathrm{cm} respectively, find the weight of the shell
Q4MathsUnit 8: Integral Calculus
Assertion If a>0a>0 and b2−4ac<0.b^{2}-4 a c<0 . then the value of the integral ∫dxax2+bx+c\int \frac{d x}{a x^{2}+b x+c} will be of the type μtan⁡−1(x+AB)+\mu \tan ^{-1}\left(\frac{x+A}{B}\right)+ C;C ; where A,B,C,μA, B, C, \mu are constant. Reason f(a>0,b2−4ac<0, then ax2+bx+f\left(a>0, b^{2}-4 a c<0, \text { then } a x^{2}+b x+\right. cc can be written as sum of two squares.

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