JEE Mains · Maths · STD 12 - 7.1 indefinite integral
Let\(\int \frac{2-\tan x}{3+\tan x} d x=\frac{1}{2}\left(\alpha x+\log _e|\beta \sin x+\gamma \cos x|\right)+C\), where \(\mathrm{C}\) is the constant of integration. Then \(\alpha+\frac{\gamma}{\beta}\) is equal to :
- A \(3\)
- B \(1\)
- C \(4\)
- D \(7\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
\( \int \frac{2-\tan x}{3+\tan x} d x=\int \frac{2 \cos x-\sin x}{3 \cos x+\sin x} d x \) \( 2 \cos x-\sin x=A(3 \cos x+\sin x)+B(\cos x-3 \sin x) \) \( 3 A+B=2 \) \( A-3 B=-1\) \( \Rightarrow \mathrm{A}=\frac{1}{2}, \mathrm{~B}=\frac{1}{2} \)…
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
- Let the plane \(P: 4 x-y+z=10\) be rotated by an angle \(\frac{\pi}{2}\) about its line of intersection with the plane \(x+y-z=4\). If \(\alpha\) is the distance of the point \((2,3,-4)\) from the new position of the plane \(P\), then \(35 \alpha\) isJEE Mains 2023 Hard
- Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation \(\cos ^{-1}(x)-2 \sin ^{-1}(x)=\cos ^{-1}(2 x)\) is equal to.JEE Mains 2022 Hard
- Let two fair six-faced dice \(A\) and \(B\) be thrown simultaneously. If \(E_1\) is the event that die \(A\) shows up four, \(E_2 \) is the event that die \(B\) shows up two and \(E_3\) is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true \(?\)JEE Mains 2016 Hard
- The sum of all the \(4 -\) digit distinct numbers that can be formed with the digits \(1,2,2\) and \(3\) isJEE Mains 2021 Medium
- Let \(f : S \rightarrow S\) where \(S =(0, \infty)\) be a twice differentiable function such that \(f ( x +1)= xf ( x )\) If \(g: S \rightarrow R\) be defined as \(g(x)=\log _{e} f(x),\) then the value of \(\mid g "(5)- g "(1) \mid\) is equal to :JEE Mains 2021 Hard
- The set of all values of \(k\) for which \(\left(\tan ^{-1} x \right)^{3}+\left(\cot ^{-1} x \right)^{3}= k \pi^{3}, x \in R\), is the intervalJEE Mains 2022 Hard
More PYQs from JEE Mains
- If \(a_1, a_2, a_3 …………\) an are in \(A.P\) and \(a_1 + a_4 + a_7 + …………… + a_{16} = 114\), then \(a_1 + a_6 + a_{11} + a_{16}\) is equal toJEE Mains 2019 Medium
- Let \(a, b , c \in R\) be such that \(a ^{2}+ b ^{2}+ c ^{2}=1\) If \(a \cos \theta=b \cos \left(\theta+\frac{2 \pi}{3}\right)=\operatorname{ccos}\left(\theta+\frac{4 \pi}{3}\right)\) where \(\theta=\frac{\pi}{9},\) then the angle between the vectors \(a \hat{i}+b \hat{j}+c \hat{k}\) and \(b \hat{i}+c \hat{j}+a \hat{k}\) isJEE Mains 2020 Medium
- Let \(f, g: N \rightarrow N\) such that \(f(n+1)=f(n)+f(1)\) \(\forall \, n \in N\) and \(g\) be any arbitrary function. Which of the following statements is \(NOT\) true ?JEE Mains 2021 Medium
- Let \(\mathrm{n}>2\) be an integer. Suppose that there are \(n\) Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest stations is connected by blue line, whereas all remaining pairs of stations are connected by red line. If the number of red lines is \(99\) times the number of blue lines, then the value of \(n\) isJEE Mains 2020 Medium
- Given below are two statements:
Statement I: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x}{1+|x|}\) is one-one.
Statement II: The function \(f:R\rightarrow R\) defined by \(f(x)=\frac{x^{2}+4x-30}{x^{2}-8x+18}\) is many-one.
In the light of the above statements, choose the correct answer from the options given below :JEE Mains 2026 Easy - The number of bijective functions \(f :\{1,3,5, 7, \ldots \ldots . .99\} \rightarrow\{2,4,6,8, \ldots \ldots, 100\}\), such that \(f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \ldots f(99), \quad\) isJEE Mains 2022 Hard