MHT CET · Maths · Indefinite Integration
\(\int_0^3 \frac{\mathrm{~d} x}{(x+2) \sqrt{x+1}}=\)
- A \(\tan ^{-1}\left(\frac{1}{3}\right)\)
- B \(2 \tan ^{-1}\left(\frac{1}{3}\right)\)
- C \(3 \tan ^{-1}\left(\frac{1}{3}\right)\)
- D \(4 \tan ^{-1}\left(\frac{1}{3}\right)\)
Answer & Solution
Correct Answer
(B) \(2 \tan ^{-1}\left(\frac{1}{3}\right)\)
Step-by-step Solution
Detailed explanation
Let \(u = \sqrt{x+1}\). \(x = u^2-1 \implies dx = 2u \,du\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let two non-collinear unit vectors \(\hat{a}\) and \(\hat{b}\) form an acute angle. A point P moves, so that at any time \(t\) the position vector \(\overline{\mathrm{OP}}\), where O is the origin, is given by \(\hat{a} \cos t+\hat{b} \sin t\). When \(P\) is farthest from origin O , let M be the length of \(\overline{\mathrm{OP}}\) and \(\hat{\mathrm{u}}\) be the unit vector along \(\overline{\mathrm{OP}}\), thenMHT CET 2024 Hard
- If \(\mathrm{A}+\mathrm{B}=\left[\begin{array}{cr}1 & \tan \frac{\theta}{2} \\ -\tan \frac{\theta}{2} & 1\end{array}\right]\) where A is symmetric and B is skew-symmetric matrix, then the matrix \(\left(A^{-1} B+A B^{-1}\right)\) at \(\theta=\frac{\pi}{6}\) is given byMHT CET 2024 Hard
- If \(\triangle \mathrm{ABC}\) is right angled at \(\mathrm{A}\), where \(\mathrm{A} \equiv(4,2, x), \mathrm{B} \equiv(3,1,8)\) and \(\mathrm{C} \equiv(2,-1,2)\), then the value of \(x\) isMHT CET 2023 Easy
- For all real \(x\), the vectors \(C x \hat{i}-6 \hat{j}-3 \hat{k}\) and \(x \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+2 \mathrm{C} x \hat{\mathrm{k}}\) make an obtuse angle with each other, then the value of C can be inMHT CET 2024 Medium
- The number of discontinuities of the greatest integer function \(\mathrm{f}(x)=[x], x \in\left(-\frac{7}{2}, 100\right)\)MHT CET 2023 Easy
- If \(\int \frac{x+1}{\sqrt{2 x-1}} \mathrm{~d} x=f(x) \sqrt{2 x-1}+C\), where \(C\) is an arbitrary constant, then \(f(x)\) is equal toMHT CET 2022 Medium
More PYQs from MHT CET
- Five capacitors, each of capacitance 'C' are connected as shown in the figure. The ratio of equivalent capacitance between \(P\) and \(R\) and the equivalent capacitance between \(P\) and \(Q\) is
MHT CET 2025 Medium - Two gases A and B are at absolute temperatures 350 K and 420 K respectively. The ratio of average kinetic energy of the molecules of gas \(B\) to that of gas \(A\) isMHT CET 2025 Easy
- Based on the graph given below, identify the INCORRECT statements.
MHT CET 2023 Hard - Numbers are selected at random, one at a time from the two-digit numbers \(00,01,02\), -------, 99 with replacement. An event E occurs only if the product of the two digits of a selected number is 24 . If four numbers are selected, then probability, that the event E occurs at least 3 times, isMHT CET 2025 Medium
- Identify the product (A) obtained in the following reaction.
Phenol + concentrated Nitric acid \(\underset{\mathrm{H}_2 \mathrm{SO}_4}{\stackrel{\text { Concentrad }}{\longrightarrow}} \mathrm{A}\)MHT CET 2021 Medium - A stationary wave is represented by \(\mathrm{y}=10 \sin \frac{\pi \mathrm{x}}{4} \cos 20 \pi \mathrm{t}\) where ' \(\mathrm{x}\) ' and ' \(\mathrm{y}\) ' are
expressed in \(\mathrm{cm}\) and \(^{\prime} t^{\prime}\) in second. Distance between two consecutive nodes isMHT CET 2020 Medium