AP EAMCET · Maths · Indefinite Integration
\(\int \frac{5 x^2+3}{x^2\left(x^2-2\right)} d x=\)
- A \(\frac{13}{2 \sqrt{2}} \log \left|\frac{\sqrt{2}-x}{\sqrt{2}+x}\right|+\frac{3}{2 x}+C\)
- B \(\frac{13}{4 \sqrt{2}} \log \left|\frac{x+\sqrt{2}}{x-\sqrt{2}}\right|+\frac{3}{2 x}+C\)
- C \(\frac{13}{4 \sqrt{2}} \log \left|\frac{x-\sqrt{2}}{x+\sqrt{2}}\right|+\frac{3}{2 x}+C\)
- D \(\frac{5}{3 \sqrt{2}} \log \left|\frac{x+\sqrt{2}}{x-\sqrt{2}}\right|+\frac{3}{5} x+C\)
Answer & Solution
Correct Answer
(C) \(\frac{13}{4 \sqrt{2}} \log \left|\frac{x-\sqrt{2}}{x+\sqrt{2}}\right|+\frac{3}{2 x}+C\)
Step-by-step Solution
Detailed explanation
Let, \(I=\int \frac{5 x^2+3}{x^2\left(x^2-2\right)} d x\) Put \(x^2=y\). Then, \[ \begin{aligned} & 5 y+3=(y-2) A+y B \\ & 5 y+3=y(A+B)-2 A \end{aligned} \] On comparing the coefficients, we get \(A+B=5\) and \(3=-2 A\) \(A=\frac{-3}{2}\) and \(B=\frac{13}{2}\) Thus,…
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
- The number of straight lines that can be drawn through the point \((-3,4)\) which are at a distance of 5 units from the point \((2,-8)\) isAP EAMCET 2023 Medium
- The length of the intercept on the line by the circle isAP EAMCET 2022 Medium
- Let \(a, b, c, d \in R\). If the equations \(2 b x^2+3 c x-d=0\) and \(2 a x^2+3 b x+4 c=0\) have a common root and \(\frac{4 b c+a d}{k\left(b^2-a c\right)}=\frac{b d+4 c^2}{4 b c+a d^{\prime}}\), then \(k=\)AP EAMCET 2019 Medium
- \(\int \frac{x^3-x^2+x-1}{x-1} d x\) is equal toAP EAMCET 2021 Easy
- The vectors \(\mathbf{a}=2 \hat{i}+3 \hat{j}+6 \hat{k}\) and \(\mathbf{b}\) are collinear and \(|\mathbf{b}|=2 \mathrm{l}\), then \(\mathbf{b}=\)AP EAMCET 2022 Easy
- If \(A_n=\int_{\frac{\pi}{2}} e^{-x} \cdot \cos ^n x d x\), then \(\frac{A_4-A_6}{A_4}=\)AP EAMCET 2019 Medium
More PYQs from AP EAMCET
- If \(\alpha, \beta\) are acute angles such that \(\sin \beta=2 \sin \alpha\) and \(3 \cos \beta=2 \cos \alpha\), then \(\sec (\alpha+\beta)=\)AP EAMCET 2023 Hard
- \(\int \frac{x-1}{(x+1) \sqrt{x^3+x^2+x}} d x=\)AP EAMCET 2019 Hard
- In the following reactions (i) and (ii) , the number of moles of chlorine gas released respectively areAP EAMCET 2021 Easy
- In a \(\triangle \mathrm{ABC}\) if \(a=26, b=30, \cos C=\frac{63}{65}\) then \(C=\)AP EAMCET 2024 Medium
- The interval in which \(y=\ln (\ln (x)), x>1\) is decreasing isAP EAMCET 2020 Easy
- If slope of one line of \(a x^2+4 x y+y^2=0\) is 3 times the other, then the value of ' \(a\) ' isAP EAMCET 2020 Easy