TS EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{(x-1)^{\frac{3}{4}}(x+2)^{\frac{5}{4}}}=\)
- A \(\frac{4}{3}\left(\frac{x-1}{x+2}\right)^{\frac{1}{4}}+c\)
- B \(\frac{3}{4}\left(\frac{x-1}{x-2}\right)^{\frac{1}{4}}+c\)
- C \(\frac{4}{3}\left(\frac{x+2}{x-1}\right)^{\frac{1}{4}}+c\)
- D \(\frac{3}{4}\left(\frac{x-2}{x-1}\right)^{\frac{1}{4}}+c\)
Answer & Solution
Correct Answer
(A) \(\frac{4}{3}\left(\frac{x-1}{x+2}\right)^{\frac{1}{4}}+c\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{d x}{(x-1)^{\frac{3}{4}}(x+2)^{\frac{5}{4}}}\) \[ \begin{aligned} & =\int \frac{(x-1)^{\frac{-3}{4}} d x}{(x+2)^{\frac{-3}{4}}\left(x+2^2\right)} \\ & =\int\left(\frac{x-1}{x+2}\right)^{\frac{-3}{4}}\left(\frac{1}{x+2}\right)^2 d x \end{aligned} \] Let…
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 the sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the area (in sq. units) of that triangle isTS EAMCET 2020 Medium
- Let \(\mathrm{m}, \mathrm{n}, \mathrm{p}, \mathrm{q}\) be four positive integers. If \(\int_0^{2 \pi} \sin ^m x \cos ^n x d x=4 \int_0^{\pi / 2} \sin ^m x \cos ^n x d x\), \(\int_0^{2 \pi} \sin ^p x \cos ^n x d x=0, \int_0^\pi \sin ^p x \cos ^q x d x=0, \mathrm{a}=\mathrm{m}+\mathrm{n}+\mathrm{p}\) and \(\mathrm{b}=\mathrm{m}+\mathrm{n}+\mathrm{q}\), thenTS EAMCET 2025 Hard
- Two tangents are drawn from the point \((-1,-2)\) to the parabola \(\mathrm{y}^2=4 \mathrm{x}\). If \(\theta\) is the angle between these tangents, then \(\tan \theta=\)TS EAMCET 2023 Medium
- An integrating factor of the differential equation \(\left(1-x^2\right) \frac{d y}{d x}+x y=\frac{x^4}{\left(1+x^5\right)}\left(\sqrt{1-x^2}\right)^3\) isTS EAMCET 2012 Medium
- If , then the value of at , isTS EAMCET 2022 Easy
- Let the slope of a diameter of a circle of radius units be . If is the centre of the circle, and thenTS EAMCET 2022 Easy
More PYQs from TS EAMCET
- If \(\sin h(\log x)=-2\) then \(x=\)TS EAMCET 2023 Hard
- The mid-point of the chord of the circle \(x^2+y^2-6 x+4 y-12=0\) drawn parallel to the tangent at \((-1,1)\) and at a distance of one unit from the tangent isTS EAMCET 2020 Hard
- The monomer which is present in both Bakelite and Melamine polymers isTS EAMCET 2024 Medium
- The time required to raise the temperature of 3 litre of water from \(0^{\circ} \mathrm{C}\) to \(80^{\circ} \mathrm{C}\) by a heater operated under \(200 \mathrm{~V}\) having resistance of \(50 \Omega\) is [specific heat capacity of water is \(4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\) ] [density of water \(=1000 \mathrm{~kg} / \mathrm{m}^3\) ]TS EAMCET 2022 Easy
- If \(x\) is so small that \(x^2\) and higher powers of \(x\) may be neglected, then the approximate value of \(\frac{\left(1+\frac{2}{3} x\right)^{-3}(1-15 x)^{-1 / 5}}{(2-3 x)^4}\)TS EAMCET 2015 Hard
- If \([x]\) represent greatest integer \(\leq x\) and \([\alpha, \beta]\) is the set of all real values of \(x\) for which the real function \(f(x)=\frac{\sqrt{3+x}+\sqrt{3-x}}{\sqrt{[x]+2}}\) is defined, then \(f^2(\alpha+1)+5 f^2(\beta)=\)TS EAMCET 2019 Medium