TS EAMCET · Maths · Indefinite Integration
If \(\quad \int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=f(x)-\log \left(1+x^2\right)\) then \(f(x)\) is equal to
- A \(2 x \tan ^{-1} x\)
- B \(-2 x \tan ^{-1} x\)
- C \(x \tan ^{-1} x\)
- D \(-x \tan ^{-1} x\)
Answer & Solution
Correct Answer
(A) \(2 x \tan ^{-1} x\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x\) Put \(x=\tan \theta \Rightarrow d x=\sec ^2 \theta d \theta\)…
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
- \((1-i \sqrt{3})^{2025}=\)TS EAMCET 2025 Medium
- Given that for any \(n \in \mathbf{N}\) there exist an odd integer \(q\) and a non-negative integer \(r\) such that, \(n\) can be written uniquely as \(n=q \times 2^r\). Let \(f: \mathbf{N} \rightarrow \mathbf{N} \times \mathbf{N}\) be function defined by \(f(n)=\left(r+1, \frac{q+1}{2}\right)\). Then,TS EAMCET 2020 Easy
- If \(12 \hat{\mathbf{i}}-12 \hat{\mathbf{j}}-18 \hat{\mathbf{k}},-3 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-9 \hat{\mathbf{k}}\) and \(3 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-24 \hat{\mathbf{k}}\) be the position vectors of the vertices \(A, B\) and \(C\) respectively of \(\triangle A B C\), then the position vector of the incentre of \(\triangle A B C\) isTS EAMCET 2020 Medium
- If the order and degree of the differential equation corresponding to the family of curves \(y^2=4 a(x+a)\) ( \(a\) is parameter) are \(m\) and \(n\) respectively, then \(m+n^2=\)TS EAMCET 2023 Easy
- If \[ \int \frac{x-\sin x}{1+\cos x} d x=x \tan \left(\frac{x}{2}\right)+p \log \left|\sec \left(\frac{x}{2}\right)\right|+C, \] then \(p\) is equal toTS EAMCET 2013 Medium
- The mid-point of a chord of the ellipse \(x^2+4 y^2-2 x+20 y=0 \quad\) is \((2,-4)\). The equation of the chord isTS EAMCET 2013 Medium
More PYQs from TS EAMCET
- The refractive index of the material of a double convex lens is 1.5 and its focal length is \(5 \mathrm{~cm}\). If the radii of curvature are equal, the value of the radius of curvature (in \(\mathrm{cm}\) ) isTS EAMCET 2007 Medium
- A circular loop and a square loop are formed from two wires of same length and cross section. Same current is passed through them. Then, the ratio of their dipole moments isTS EAMCET 2015 Easy
- A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then semi vertical angle of the cone isTS EAMCET 2024 Medium
- A particle moving along \(X\)-axis has acceleration \(f\) at time \(t\) given by \(f=f_0\left(1-\frac{t}{T}\right)\), where \(f_0\) and \(T\) are constants. The particle at \(t=0\) has zero velocity. In the time interval between \(t=0\) and the instant when \(f=0\), the particle's velocity isTS EAMCET 2020 Medium
- The value that should be assigned to \(f(0)\) so that the function \(f(x)=(x+1)^{\cot x}\) is continuous at \(x=0\), isTS EAMCET 2015 Easy
- The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of 52 playing cards isTS EAMCET 2022 Medium