CUET · MATHS · PYQ PAPER 2023
\(\int x^2 \tan ^{-1} x d x\)=
- A \(\frac{x^3}{3} \tan ^{-1} x-\frac{x^2}{6}+\frac{1}{6} \log \left|x^2+1\right|+C\)
- B \(\frac{x^3}{3} \tan ^{-1} x+\frac{x^2}{6}+\frac{1}{6} \log \left|x^2+1\right|+C\)
- C \(\frac{x^3}{3} \tan ^{-1} x-\frac{x^2}{6}-\frac{1}{6} \log \left|x^2+1\right|+C\)
- D \(\frac{x^3}{3} \tan ^{-1} x+\frac{x^2}{6}-\frac{1}{6} \log \left|x^2+1\right|+C\)
Answer & Solution
Correct Answer
(A) \(\frac{x^3}{3} \tan ^{-1} x-\frac{x^2}{6}+\frac{1}{6} \log \left|x^2+1\right|+C\)
Step-by-step Solution
Detailed explanation
\(\int x^2 \tan ^{-1} x d x = \tan ^{-1} x \cdot \frac{x^3}{3} - \int \frac{x^3}{3} \cdot \frac{1}{1+x^2} d x\) \(= \frac{x^3}{3} \tan ^{-1} x - \frac{1}{3} \int \frac{x^3}{1+x^2} d x\) \(= \frac{x^3}{3} \tan ^{-1} x - \frac{1}{3} \int \left(x - \frac{x}{1+x^2}\right) d x\)…
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
- If \(V=\frac{4 \pi r^3}{3}\), at what rate in cubic units \(/ sec\) is V increasing when \(r=10\), and \(\frac{d r}{d t}=0.01 ?\)CUET 2023 Easy
- Which of the following matrices is not invertible?CUET 2023 Medium
- A manufacturer can sell x items at a price of mp 3x + 5 each. The cost price of x items is ₹\(x^2\ + 5x.
If z is the number of items she should sell to get no profit and no loss, then:CUET 2023 Easy - The maximum value of the determinant of the matrix \(\left[\begin{array}{ccc}1 & 1 & 1 \\ 1 & 1+\sin x & 1 \\ 1+\cos x & 1 & 1\end{array}\right]\)
(where \(x\) is real) is :CUET 2025 Hard - From a container full of orange juice, 7.5 liters was drawn out and replaced by soda water.
This process is repeated 5 more time.
The ratio of quantity of orange juice and soda water left in the container is 4:5.
How much liter of orange juice did the container originally had?
(Use \((0.44)^{1 / 6}\) = 0.802)CUET 2025 Medium - The value/s of \(\lambda\) for which the given system of equations will have infinitely many solutions \(x+y-6 z=0 ; \lambda x-y+2 z=0 ;-3 x+\lambda y+2 z=0\), is/are:CUET 2023 Easy
More PYQs from CUET
- The electrochemical cells \(Zn \left| Zn ^{2+} \| Cu ^{2+}\right| Cu\) and \(Fe ^{-} Fe ^{2+} \| Cu ^{2+} \mid Cu\) are connected in series. What will be the net emf of the cell at \(25^{\circ} C\) ? Given: \(E ^{\circ}\) of \(Zn ^{2+} \mid Zn =-0.76 V ; \quad E ^{\circ}\) of \(Cu ^{2+} \mid Cu =+0.34 V ; \quad E ^{\circ}\) of \(Fe ^{2+} \mid Fe =-0.41 V\)CUET 2023 Easy
- Match List - I with List - II.
List - I List - II (A) Microwaves (I) used in cell phone communication (B) Radiowaves (II) used in remote sensing (C) UV rays (III) used in aircraft navigation (D) Infrared rays (IV) causes tanning of skin
Choose the correct answer from the options given below :CUET 2023 Easy - If \(y=a+b(x-2022)\) is a straight line trend using the least square method for the following data
Then the value of \(\frac{a}{b}\) is:Year(x) 2020 2021 2022 2023 2024 Profit(Rs. '000)(y) 2 3 4 5 2 CUET 2025 Medium - An induced emf is produced when a magnet is plunged into a coil. The magnitude of the induced emf is independent ofCUET 2025 Medium
- The equation of tangent to the curve given by \(x=a \sin ^3 t, y=b \cos ^3 t\) at a point where \(t=\frac{\pi}{2}\) is :CUET 2023 Hard
- "Match the reaction order with their examples in List-II.
List-I List-II (A) First order reaction (I) \(\text{C}_{12}\text{H}_{22}\text{O}_{11} + \text{H}_2\text{O} \xrightarrow{\text{H}^+} \text{C}_6\text{H}_{12}\text{O}_6 + \text{C}_6\text{H}_{12}\text{O}_6\) (B) Zero order reaction (II) \(\text{N}_2\text{O}_5 \rightarrow 2\text{NO}_2 + \frac{1}{2}\text{O}_2\) (C) Pseudo first order reaction (III) \(\text{CH}_3\text{COOC}_2\text{H}_5 + \text{NaOH} \rightarrow \text{CH}_3\text{COONa} + \text{C}_2\text{H}_5\text{OH}\) (D) Second order reaction (IV) \(2\text{NH}_3\text{(g)} \xrightarrow{\text{1130 K}\text{ Pt}} \text{N}_2\text{(g)} + 3\text{H}_2\text{(g)}\)
Choose the correct answer from the options given below:"CUET 2023 Easy