AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x\)
- A \(\frac{1+2 x^2+2 x^4}{2 x^2}+c\)
- B \(\frac{\left(1+2 x^2+2 x^4\right)^{\frac{1}{2}}}{2 x^2}+c\)
- C \(\frac{1-2 x^2+2 x^4}{2 x^2}+c\)
- D \(\frac{\left(1-2 x^2+2 x^4\right)^{\frac{1}{2}}}{2 x^2}+c\)
Answer & Solution
Correct Answer
(D) \(\frac{\left(1-2 x^2+2 x^4\right)^{\frac{1}{2}}}{2 x^2}+c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x\) Divide numerator and denominator by \(x^5\).…
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
- \(\int \frac{e^{2 x}}{\sqrt[4]{e^x+1}} d x=\)AP EAMCET 2024 Easy
- A bag contains 3 white, 2 blue and 5 red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red isAP EAMCET 2022 Easy
- If \(\frac{y}{x} \cos ^4 \alpha+\frac{x}{y} \sin ^4 \alpha=2 \sin ^2 \alpha \cdot \cos ^2 \alpha\), then \(\frac{d y}{d x}=\)AP EAMCET 2022 Hard
- If \(x>0, y>0, z>0, x y+y z+z x < 1\) and if \(\tan ^{-1} x+\tan ^{-1} y+\tan ^{-1} z=\pi\), then \(x+y+z\) equals toAP EAMCET 2014 Medium
- If \(f(x)=x^{\mathrm{x}}\), then the interval in which \(f(x)\) decreases isAP EAMCET 2024 Medium
- If \(I_n=\int \tan ^n x d x(n>1)\), then \(I_4+I_6=\)AP EAMCET 2023 Easy
More PYQs from AP EAMCET
- If \(\bar{a}=\bar{i}+4 \bar{j}-4 \bar{k}, \bar{b}=-2 \bar{i}+5 \bar{j}-2 \bar{k}\) and \(\bar{c}=3 \bar{i}-2 \bar{j}-4 \bar{k}\) are three vectors such that \((\bar{b} \times \bar{c}) \times \bar{a}=x \bar{i}+y \bar{j}+z \bar{k}\) then \(x+y-z=\)AP EAMCET 2025 Medium
- The value of \(x\) in \(\left(0, \frac{\pi}{2}\right)\) satisfying the equation \((\sin x)(\cos x)=\frac{1}{4}\) isAP EAMCET 2020 Easy
- A uniform metal wire carries a current of \(2 \mathrm{~A}\) when an ideal cell of \(3.4 \mathrm{~V}\) is connected across it. The wire has mass \(8.92 \times 10^{-3} \mathrm{~kg}\), density \(8.92 \times 10^3 \mathrm{kgm}^{-3}\) and resistivity \(1.7 \times 10^{-8} \Omega \mathrm{m}\). Then the length of the wire isAP EAMCET 2023 Medium
- If \(y=\log (\cosh x)\) then \(\frac{d^2 y}{d x^2}=\)AP EAMCET 2020 Easy
- The number of distinct real solutions for the equation \(\left|x^2+2 x-8\right|+x-2=0\) isAP EAMCET 2018 Medium
- Two square shaped metal plates of side \(1 \mathrm{~m}\), kept \(0.01 \mathrm{~m}\) apart in air form a parallel plate capacitor. It is connected to a battery of \(500 \mathrm{~V}\). The plates of the capacitor are then immersed in an insulting oil by lowering the plates vertically with a speed of \(0.001 \mathrm{~ms}^{-1}\). If the dielectric constant of the oil is 11 , then current drawn from the battery during this process isAP EAMCET 2023 Hard