MHT CET 2026 16th April Evening Shift | Indefinite Integration Question 34 | Mathematics

If $a > 0, b > 0$ and $\int\dfrac{1}{ax^2 + b}dx = \dfrac{1}{\sqrt{6}}\tan^{-1}\left(\dfrac{\sqrt{2}x}{\sqrt{3}}\right) + c$, then $\int\dfrac{1}{bx^2 + a}dx = \ldots$

$-\dfrac{1}{\sqrt{6}}\tan^{-1}\left(\dfrac{\sqrt{2}x}{\sqrt{3}}\right) + c$

$\dfrac{1}{\sqrt{6}}\tan^{-1}\left(\dfrac{\sqrt{3}x}{\sqrt{2}}\right) + c$

$-\sqrt{6}\,\tan^{-1}\left(\dfrac{\sqrt{2}x}{\sqrt{3}}\right) + c$

$\sqrt{6}\,\tan^{-1}\left(\dfrac{\sqrt{3}x}{\sqrt{2}}\right) + c$

MHT CET 2026 16th April Morning Shift

MCQ (Single Correct Answer)

-0

$\displaystyle\int \dfrac{(x + 1)(x + \log x)^2}{x}\,dx =$

$\left(\dfrac{x + \log x}{x}\right)^2 + c$, where c is the constant of integration

$\dfrac{(x + \log x)^2}{x} + c$, where c is the constant of integration

$\dfrac{(x + \log x)^3}{3} + c$, where c is the constant of integration

$\dfrac{(x + \log x)^3}{3x} + c$, where c is the constant of integration

MHT CET 2026 16th April Morning Shift

MCQ (Single Correct Answer)

-0

$\displaystyle\int \cot^4 x\,dx$ is equal to

$\dfrac{\cot^3 x}{3} - \cot x + x + c$

$\dfrac{\cot^3 x}{3} + \cot x + x + c$

$-\dfrac{\cot^3 x}{3} + \cot x + x + c$

$\dfrac{\cot^3 x}{3} - 2\cot x + x + c$

PREVIOUS NEXT

MHT CET Subjects

Browse all chapters by subject

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Atomic Structure States of Matter Thermodynamics Chemical Equilibrium Ionic Equilibrium Liquid Solution Redox Reactions Surface Chemistry Solid State Electrochemistry Chemical Kinetics Nuclear Chemistry

Inorganic Chemistry

Periodic Table and Periodicity Chemical Bonding and Molecular Structure Metallurgy Hydrogen and It's Compounds s-Block Elements p-Block Elements d and f Block Elements Coordination Compounds Environmental Chemistry

Organic Chemistry

IUPAC Nomenclatures General Organic Chemistry Isomerism Hydrocarbons Haloalkanes and Haloarenes Alcohol, Phenols and Ethers Aldehyde and Ketone Carboxylic Acids and Its Derivatives Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical Organic Chemistry