AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x-1}{(x+1) \sqrt{x^3+x^2+x}} d x=\)
- A \(2 \tan ^{-1}\left(\sqrt{\frac{1+x+x^2}{x}}\right)+c\)
- B \(\tan ^{-1}\left(\sqrt{\frac{1+x+x^2}{x}}\right)+c\)
- C \(\tan ^{-1}\left(\sqrt{\frac{x}{1+x+x^2}}\right)+c\)
- D \(\tan ^{-1}\left(\sqrt{\frac{1+x^2}{x}}\right)+c\)
Answer & Solution
Correct Answer
(A) \(2 \tan ^{-1}\left(\sqrt{\frac{1+x+x^2}{x}}\right)+c\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int \frac{x-1}{(x+1) \sqrt{x^3+x^2+x}} d x \\ & \quad=\int \frac{x^2-1}{(x+1)^2 x \sqrt{1+\frac{1}{x}+x}} d x \\ & \quad=\int \frac{x^2-1}{\left(1+1+\frac{1}{x}+x\right) x^2 \sqrt{1+\frac{1}{x}+x}} d x \\ & \quad=\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
- If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{c}=4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+7 \hat{\mathbf{k}}\), then the vector \(r\) satisfying \(r \times b=c \times b\) and \(r . a=0\) isAP EAMCET 2015 Medium
- The equation of a line though the point (1, 2) whose distance from the point (3, 1) has the greatest value isAP EAMCET 2021 Medium
- The smallest positive root of the equation \(\tan x-x=0\) lies in the intervalAP EAMCET 2018 Easy
- The domain of the real valued function \(f(x)=\log _2 \log _3 \log _5\left(x^2-5 x+11\right)\) isAP EAMCET 2024 Easy
- If \(\tan \mathrm{B}=\frac{2 \sin \mathrm{A} \sin \mathrm{C}}{\sin (\mathrm{A}+\mathrm{C})}\), then \(\tan \mathrm{A}, \tan \mathrm{B}\) and \(\tan \mathrm{C}\) are inAP EAMCET 2023 Medium
- A random variable \(X\) has the following distribution
\begin{array}{lllllllll}
\hline \begin{array}{l}
Values of \\
X(x)
\end{array} & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\
\hlineP(X=x) \quad 0 & k & 2 k & 2 k & 3 k & k^2 & 2 k^2 & 7 k^2+k \\
\hline
\end{array}AP EAMCET 2018 Medium
More PYQs from AP EAMCET
- Let \(S\) be the set of all quadratic equations of the form \(x^2+b x+c=0\), where \(b, c \in\{1,2,3\), \(4,5,6\}\). If an equation is selected at random from \(S\), then the probability that the equation has real roots isAP EAMCET 2021 Medium
- A block of mass 1.5 kg kept on a rough horizontal surface is given a horizontal velocity of \(10 \mathrm{~ms}^{-1}\). If the block comes to rest after travelling a distance of 12.5 m , the coefficient of kinetic friction between the surface and the block is (Acceleration due to gravity \(=10 \mathrm{~ms}^{-2}\) )AP EAMCET 2024 Easy
- A uniform rod of length and density is revolving about a vertical axis passing through its one end. If is the angular velocity of the rod then the centrifugal force per unit area of the rod isAP EAMCET 2019 Medium
- If the coefficients of \(r\) th and \((r+1)\) th terms in the expansion of \((3+7 x)^{29}\) are equal, then \(r\) is equal toAP EAMCET 2011 Easy
- If the equation of the tangent of the hyperbola \(5 x^2-9 y^2-20 x-18 y-34=0\) which makes an angle \(45^{\circ}\) with the positive X -axis in positive direction is \(x+b y+c=0\) then \(b^2+c^2=\)AP EAMCET 2025 Hard
- If \(|\mathbf{a}|=1,|\mathbf{b}|=2\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then \(\{(\mathbf{a}+3 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})\}^2\) is equal toAP EAMCET 2011 Easy