AP EAMCET · Maths · Indefinite Integration
\[
\int \operatorname{Tan}^{-1}\left(x^{\frac{1}{3}}\right) d x=
\]
- A \(\frac{1}{2} \log \left(1+x^{\frac{2}{3}}\right)-\frac{1}{2} x^{\frac{2}{3}}+c\)
- B \(\text { 2. } x \operatorname{Tan}^{-1}\left(x^{\frac{1}{3}}\right)-\frac{1}{2} x^{\frac{2}{3}}+c\)
- C \(\frac{1}{2} \log \left(1+x^{\frac{1}{3}}\right)-\frac{1}{2} x^{\frac{2}{3}}+c\)
- D \(x \operatorname{Tan}^{-1}\left(x^{\frac{1}{3}}\right)+\frac{1}{2} \log \left(1+x^{\frac{2}{3}}\right)-\frac{1}{2} x^{\frac{2}{3}}+c\)
Answer & Solution
Correct Answer
(D) \(x \operatorname{Tan}^{-1}\left(x^{\frac{1}{3}}\right)+\frac{1}{2} \log \left(1+x^{\frac{2}{3}}\right)-\frac{1}{2} x^{\frac{2}{3}}+c\)
Step-by-step Solution
Detailed explanation
No solution. Refer to answer key.
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 the point \((a, 2 a)\) is an interior point of the region bounded by the parabola \(y^2=16 x\) and the double ordinate through focus, thenAP EAMCET 2021 Easy
- Which of the following is a fourth root of
\[
\frac{1}{2}+\frac{i \sqrt{3}}{2} \text { ? }
\]AP EAMCET 2021 Medium - \(a, b, c\) are the sides of a scalene triangle \(A B C\). If angles \(\alpha, \beta, \gamma\) lie between 0 and \(\pi\) such that \(\cos \alpha=\frac{a}{b+c}, \cos \beta=\frac{b}{c+a}\) and \(\cos \gamma=\frac{c}{a+b}\), then \(\tan ^2 \frac{\alpha}{2}+\tan ^2 \frac{\beta}{2}+\tan ^2 \frac{\gamma}{2}=\)AP EAMCET 2019 Medium
- If \(\bar{a}=2 \bar{i}+\bar{j}-3 \bar{k}, \bar{b}=\bar{i}-2 \bar{j}+\bar{k}, \bar{c}=-\bar{i}+\bar{j}-4 \bar{k}, \bar{d}=\bar{i}+\bar{j}+p \bar{k}\), where \(p\) is a positive real number and \(|(\bar{a} \times \bar{b}) \times(\bar{c} \times \bar{d})|=5 \sqrt{114}\), then a value of \(p\) isAP EAMCET 2017 Medium
- is a square with side units and is the origin. If the equation of the circle circumscribing the square is thenAP EAMCET 2018 Easy
- Let \(\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}\) defined by \(\mathrm{f}(\mathrm{x})=5 \mathrm{x}^4+2\). ThenAP EAMCET 2022 Easy
More PYQs from AP EAMCET
- The area (in sq. units) bounded by \(x=4, y=-4\) and \(y=x\) isAP EAMCET 2023 Easy
- Which of the following equations represents the velocity of the ejected electrons when a metal is made to strike with light of frequency and the threshold frequency of the metal is mass of electron and is Planck's constant).AP EAMCET 2019 Medium
- The radiation of energy ' \(E\) ' falls normally on a perfectly reflecting surface. The momentum transferred to the surface isAP EAMCET 2024 Easy
- In \(\triangle \mathrm{ABC}\), if the sides \(a, b, c\) are in geometric progression and the largest angle exceeds the smallest angle by \(60^{\circ}\), then \(\cos B\) is equal toAP EAMCET 2016 Medium
- Arrange N, S, O and F in order of decreasing electron gain enthalpy.AP EAMCET 2021 Easy
- If \(a, b, c\) are distinct positive real numbers, then the value of the determinant \(\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|\) isAP EAMCET 2016 Easy