WBJEE · Maths · Indefinite Integration
\(\int \frac{x^{2}-1}{x^{4}+3 x^{2}+1} d x(x>0)\) is
- A \(\tan ^{-1}\left(x+\frac{1}{x}\right)+C\)
- B \(\tan ^{-1}\left(x-\frac{1}{x}\right)+C\)
- C \(\log _{e}\left|\frac{x+\frac{1}{x}-1}{x+\frac{1}{x}+1}\right|+C\)
- D \(\log _{e}\left|\frac{x-\frac{1}{x}-1}{x-\frac{1}{x}+1}\right|+C\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1}\left(x+\frac{1}{x}\right)+C\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{x^{2}-1}{x^{4}+3 x^{2}+1} d x\) \(=\int \frac{1-1 / x^{2}}{x^{2}+3+1 / x^{2}} d x\) \(=\int \frac{1-1 / x^{2}}{\left(x^{2}+\frac{1}{x^{2}}\right)+3} d x\) \(=\int \frac{1-1 / x^{2}}{\left(x+\frac{1}{x}\right)^{2}-2+3} d x\)…
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
- Let \(t_{n}\) denotes the nth term of the infinite series \(\frac{1}{1 !}+\frac{10}{2 !}+\frac{21}{3 !}+\frac{34}{4 !}+\frac{49}{5 !}+\ldots .\) Then \(\lim _{n \rightarrow \infty} t_{n}\) isWBJEE 2014 Hard
- If \(A^2-A+I=0\), then the inverse of the matrix \(A\) isWBJEE 2009 Easy
- If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \(a x^{2}+b x+c=0\) and \(3 b^{2}=16 a c\) thenWBJEE 2013 Medium
- Let \(a, b, c\) and \(d\) be any four real numbers. Then. \(a^{n}+b^{n}=c^{n}+d^{n}\) holds for any natural number \(n\). ifWBJEE 2015 Medium
- Let \(Q=\left(\begin{array}{cc}\cos \frac{\pi}{4} & -\sin \frac{\pi}{4} \\ \sin \frac{\pi}{4} & \cos \frac{\pi}{4}\end{array}\right)\) and\(x=\left(\begin{array}{c}\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}}\end{array}\right)\) then \(Q^{3} x\) is equal toWBJEE 2016 Medium
- If \(R\) be the set of all real numbers and \(f: R \rightarrow R\) is given by \(f(x)=3 x^{2}+1\). Then, the set \(f^{-1}([1,6])\) isWBJEE 2014 Medium
More PYQs from WBJEE
- The number of complex numbers \(\mathrm{p}\) such that \(|\mathrm{p}|=1\) and imaginary part of \(\mathrm{p}^{4}\) is 0, isWBJEE 2020 Medium
- The letters of the word 'COCHIN' are permuted and all the permutations are arranged in alphabetical order as in English dictionary. The number of words that appear before the word 'COCHIN', isWBJEE 2015 Easy
- If for the series \(a_1, a_2, a_3, \ldots\). etc, \(a_r-a_{r+1}\) bears a constant ratio with \(a_r a_{r+1} ;\) then \(a_1, a_2, a_3 \ldots\). are inWBJEE 2024 Easy
- During electrolysis of molten \(\mathrm{NaCl},\) some water was added. What will happen?WBJEE 2017 Easy
- Chlorine gas reacts with red hot calcium oxide to giveWBJEE 2013 Easy
- If the four points with position vectors \(-2\hat i+\hat j + \hat k, \hat i+\hat j+\hat k,\hat j- \hat k\) and \(\lambda \hat j + \hat k\) are coplanar, then \(\lambda\) is equal toWBJEE 2015 Easy