TS EAMCET · Maths · Indefinite Integration
\[ \int \frac{2 x+3}{\sqrt{3 x^2-2 x+1}} d x= \]
- A \(\frac{2}{3} \sqrt{3 \mathrm{x}^2-2 \mathrm{x}+1}+\frac{11}{3} \sin h^{-1}\left(\frac{3 \mathrm{x}-1}{\sqrt{2}}\right)+c\)
- B \(\frac{1}{3} \sqrt{3 x^2-2 x+1}+\frac{11}{3} \sin h^{-1}\left(\frac{\sqrt{3} \mathrm{x}-1}{\sqrt{2}}\right)+c\)
- C \(\frac{1}{3} \sqrt{3 \mathrm{x}^2-2 \mathrm{x}+1}+\frac{11}{3} \sin h^{-1}\left(\frac{3 \mathrm{x}-1}{\sqrt{3}}\right)+c\)
- D \(\frac{2}{3} \sqrt{3 \mathrm{x}^2-2 \mathrm{x}+1}+\frac{11}{3 \sqrt{3}} \sin h^{-1}\left(\frac{3 \mathrm{x}-1}{\sqrt{3}}\right)+c\)
Answer & Solution
Correct Answer
(D) \(\frac{2}{3} \sqrt{3 \mathrm{x}^2-2 \mathrm{x}+1}+\frac{11}{3 \sqrt{3}} \sin h^{-1}\left(\frac{3 \mathrm{x}-1}{\sqrt{3}}\right)+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \int \frac{2 x+3}{\sqrt{3 x^2-2 x+1}} d x=\frac{1}{3} \int \frac{6 x-2+\frac{11}{3}}{\sqrt{3 x^2-2 x+1}} d x \\ & =\frac{1}{3}\left[\int \frac{(6 x-2) d x}{\sqrt{3 x^2-2 x+1}}+\frac{11}{3} \int \frac{d x}{\sqrt{3 x^2-2 x+1}}\right] \\ & I_1=\int…
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 area of the region (in square units) bounded by the curves and , isTS EAMCET 2019 Easy
- Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife isTS EAMCET 2024 Easy
- The equation of the hyperbola which passes through the point \((2,3)\) and has the asymptotes \(4 x+3 y-7=0\) and \(x-2 y-1=0\) isTS EAMCET 2010 Medium
- In a triangle ABC, if \(\overline{\mathrm{BC}}=\bar{i}-2 \bar{j}+2 \bar{k}\) and \(\overline{\mathrm{CA}}=6 \bar{i}+3 \bar{j}-2 \bar{k}\), then the perimeter of the triangle isTS EAMCET 2025 Medium
- \(L_1 \equiv 2 x+y-3=0\) and \(L_2 \equiv a x+b y+c=0\) are two equal sides of an isosceles triangle. If \(L_3 \equiv x+2 y+1=0\) is the third side of this triangle and \((5,1)\) is a point on \(L_2\) \(=0\) then \(\frac{b^2}{|a c|}=\)TS EAMCET 2024 Hard
- If a chord of the parabola \(y^2=4 x\) passes through its focus and makes an angle \(\theta\) with the \(X\)-axis, then its length isTS EAMCET 2011 Hard
More PYQs from TS EAMCET
- If the solution of the differential equation \(\frac{d y}{d x}=\frac{2 x+3 y}{3 x-2 y}\) is \(\mathrm{y}=\mathrm{x} \tan (\mathrm{f}(\mathrm{x}))+\mathrm{c}\) then \(\mathrm{f}(\mathrm{x})=\)TS EAMCET 2023 Medium
- Consider a rod of length, with a cross-sectional area of The rod supports a , platform that hangs attached to the rod's lower end. What is the elongation of the rod under the stress ignoring the weight of the rod? Consider Young's modulus to be andTS EAMCET 2021 Medium
- \(\lim _{n \rightarrow \infty} \sum_{k=1}^n \frac{k}{n^2+k^2}=\)TS EAMCET 2019 Easy
- Which of the following is not a correct statement?TS EAMCET 2021 Hard
- Assertion \((\mathrm{A}) \operatorname{cosech}^{-1}(\mathrm{~B})=\log \left(\frac{1+\sqrt{10}}{3}\right)\) Reason (R) \(e^{\operatorname{cosech}^{-1} x}\) is a root of the quadratic equation \(x p^2-2 p-x=0\) The correct option among the following isTS EAMCET 2020 Medium
- If \(\tan A+\tan B+\cot A+\cot B=\tan A \tan B-\cot A \cot B\) and \(0^{\circ} \lt A+B \lt 270^{\circ}\), then \(A+B=\)TS EAMCET 2024 Medium