TS EAMCET · Maths · Indefinite Integration
\(\int \frac{\left(x+\sqrt{1+x^2}\right)^2}{\sqrt{1+x^2}} d x=\)
- A \(\frac{x}{\sqrt{1+x^2}}+C\)
- B \(\log \left|x+\sqrt{1+x^2}\right|+C\)
- C \(x+\sqrt{1+x^2}+C\)
- D \(\frac{\left(x+\sqrt{1+x^2}\right)^2}{2}+C\)
Answer & Solution
Correct Answer
(D) \(\frac{\left(x+\sqrt{1+x^2}\right)^2}{2}+C\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{\left(x+\sqrt{1+x^2}\right)^2}{\sqrt{1+x^2}} d x\)…
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 thenTS EAMCET 2021 Easy
- If \(m_1, m_2\) are the slopes of the tangents drawn through the point \((-1,-2)\) to the circle \((x-3)^2+(y-4)^2=4\), then \(\sqrt{3}\left|m_1-m_2\right|=\)TS EAMCET 2025 Medium
- Let \(S\) be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces (numbered 1 to 6 ) and let \(E_k=\{(a, b) \in S: a b=k\}\) for \(k \geq 1\). If \(p_k+P\left(E_k\right)\) for \(k \geq 1\), then the correct among the following, isTS EAMCET 2008 Medium
- A candidate takes three tests in succession and the probability of passing the first test is \(p\). The probability of passing each succeeding test is \(p\) or \(\frac{p}{2}\) according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, isTS EAMCET 2014 Easy
- If \(\omega\) is a complex cube root of unity, then \(\begin{aligned} & \left(\frac{1-\sqrt{3} i}{2}\right)^{2020}+\left(\frac{1+\sqrt{3} i}{2}\right)^{2026} \ & +\sin \left(\sum_{j=1}^6(j+\omega)\left(j+\omega^2\right) \frac{3 \pi}{152}\right)=\end{aligned}\)TS EAMCET 2020 Hard
- If the direction ratio of two lines are given by \(3 l m-4 l n+m n=0\) and \(l+2 m+3 n=0\), then the angle between the lines, is :TS EAMCET 2003 Easy
More PYQs from TS EAMCET
- If \(\log (1+x)-\frac{2 x}{2+x}\) is increasing, thenTS EAMCET 2002 Easy
- Relative abundance (in percentage) of \({ }^{14} \mathrm{C}\) isotope isTS EAMCET 2018 Easy
- If the tangents \(x+y+k=0\) and \(x+a y+b=0\) drawn to the circle \(S \equiv x^2+y^2+2 x-2 y+1=0\) are perpendicular to each other and \(k, b\) are both greater than 1 , then \(b-k=\)TS EAMCET 2024 Easy
- Which of the following is not a periodic property?TS EAMCET 2021 Easy
- The correct order of decreasing acidic nature of oxidesTS EAMCET 2022 Medium
- A plane \(\pi\) makes intercepts 3 and 4 respectively on \(Z\)-axis and \(X\)-axis. If \(\pi\) is parallel to \(Y\)-axis, then its equation is :TS EAMCET 2003 Medium