MHT CET · Maths · Indefinite Integration
\(\int \frac{d x}{(x+2) \sqrt{x+1}}=\)
- A \(\tan ^{-1}(\sqrt{x+1})+c\)
- B \(2 \tan ^{-1}(\sqrt{x+1})+c\)
- C \(2 \tan ^{-1}(\sqrt{x+2})+c\)
- D \(\tan ^{-1}(\sqrt{x+2})+c\)
Answer & Solution
Correct Answer
(B) \(2 \tan ^{-1}(\sqrt{x+1})+c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{d x}{(x+2) \sqrt{x+1}}\)
Put \(\sqrt{x+1}=t \Rightarrow(x+1)=t^{2}\) and \(d x=2 t d t\)
\(\therefore I=\int \frac{2 t d t}{\left(t^{2}+1\right) t}\)
\(\quad=2 \int \frac{d t}{t^{2}+1}=2 \tan ^{-1} t+c=2 \tan ^{-1}(\sqrt{x+1})+c\)
Put \(\sqrt{x+1}=t \Rightarrow(x+1)=t^{2}\) and \(d x=2 t d t\)
\(\therefore I=\int \frac{2 t d t}{\left(t^{2}+1\right) t}\)
\(\quad=2 \int \frac{d t}{t^{2}+1}=2 \tan ^{-1} t+c=2 \tan ^{-1}(\sqrt{x+1})+c\)
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
- \(\int \sec ^{\frac{2}{3}} x \cdot \operatorname{cosec}^{\frac{4}{3}} x \mathrm{~d} x=\)MHT CET 2025 Medium
- If \(\bar{a}, \overline{\mathrm{~b}}, \overline{\mathrm{c}}\) are three vectors such that \(|\bar{a}|=\sqrt{31}, 4|\overline{\mathrm{~b}}|=|\overline{\mathrm{c}}|=2\) and \(2(\bar{a} \times \bar{b})=3\left(\bar{c} \times \bar{a}\right.\) )and if the angle between \(\bar{b}\) and \(\bar{c}\) is \(\frac{2 \pi}{3}\) then \(\left|\frac{\bar{a} \times \bar{c}}{\bar{a} \cdot \bar{b}}\right|^2=\)MHT CET 2025 Hard
- If the foot of the perpendicular drawn from the origin to a plane is \(P(-1,-1,2)\), then equation of the plane isMHT CET 2025 Easy
- The order of the differential equation of all circles which lie in the first quadrant and touch both the axes is…MHT CET 2019 Easy
- …MHT CET 2019 Medium
- Angle of intersection of the curve \(r=\sin \theta+\cos \theta\) and \(r=2 \sin \theta\) is equal toMHT CET 2008 Easy
More PYQs from MHT CET
- The value of \(\lim _{x \rightarrow 0} \frac{\cos (\sin x)-\cos x}{x^{4}}\) is equal toMHT CET 2007 Hard
- In case of rotational dynamics, which one of the following statements is correct?
\([\vec{\omega}=\) angular velocity, \(\vec{v}=\) linear velocity
\(\overrightarrow{\mathrm{r}}=\) radius vector, \(\vec{\alpha}=\) angular acceleration
\(\overrightarrow{\mathrm{a}}=\) linear acceleration, \(\overrightarrow{\mathrm{L}}=\) angular momentum
\(\overrightarrow{\mathrm{p}}=\) linear momentum, \(\vec{\tau}=\) torque,
\(\overrightarrow{\mathrm{f}}=\) centripetal force \(]\)MHT CET 2024 Medium - Match the following with respect to stages of embryonic development in human.
Column I Column II a. Fully formed morula. i. By end of \(7^{\text {th }}\) day after fertilization b. Fully formed blastocyst. ii. 15 days after fertilization c. Completion of Implantation process iii. By end of \(4^{\text {th }}\) day after fertilization d. Fully formed gastrula iv. By end of \(10^{\text {th }}\) day after fertilization
Choose the correct option-MHT CET 2023 Medium - Which of the following quantified statement is true?MHT CET 2016 Easy
- Identify the outer electronic configuration of first element of first transition series.MHT CET 2022 Easy
- The period of oscillation of a second's pendulum on the planet whose mass and radius are twice that of earth willMHT CET 2022 Medium