Question:
\(∫\frac{1}{x[6(logx)^2+7logx+2]}dx=\)
\(∫\frac{1}{x[6(logx)^2+7logx+2]}dx=\)
Updated On: Apr 26, 2024
- \(\frac{1}{2}log|\frac{2logx+1}{3logx+2}|+C\)
- \(log|\frac{2logx+1}{3logx+2}|+C\)
- \(log|\frac{3logx+2}{2logx+1}|+C\)
- \(\frac{1}{2}log|\frac{3logx+2}{2logx+1}|+C\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct answer is Option (B) : \(log|\frac{2logx+1}{3logx+2}|+C\)
Was this answer helpful?
0
0
Top Questions on Integration
- If \[\int_{0}^{\pi/4} \frac{\sin^2 x}{1 + \sin x \cos x} \, dx = \frac{1}{a} \log_e \left( \frac{a}{3} \right) + \frac{\pi}{b\sqrt{3}},\]where \( a, b \in \mathbb{N} \), then \( a + b \) is equal to _____
- JEE Main - 2024
- Mathematics
- Integration
- Let \( f(x) = \begin{cases} -2, & -2 \leq x \leq 0 \\ x - 2, & 0 < x \leq 2 \end{cases} \) and \( h(x) = f(|x|) + |f(x)| \). Then \(\int_{-2}^{2} h(x) \, dx\) is equal to:
- JEE Main - 2024
- Mathematics
- Integration
- If \[ \int \cosec^5 x \, dx = \alpha \cot x \cosec x \left( \cosec^2 x + \frac{3}{2} \right) + \beta \log_e \left| \tan \frac{x}{2} \right| + C, \] where \( \alpha, \beta \in \mathbb{R} \) and \( C \) is the constant of integration, then the value of \( 8(\alpha + \beta) \) equals:
- JEE Main - 2024
- Mathematics
- Integration
- The integral \[ \int_{1/4}^{3/4} \cos\left( 2 \cot^{-1} \sqrt{\frac{1 - x}{1 + x}} \right) \, dx \] is equal to:
- JEE Main - 2024
- Mathematics
- Integration
- If the area of the region \[ \{(x,y) : 0 \leq y \leq \min\{2x, 6x - x^2\}\} \] is \( A \), then \( 12A \) is equal to \ldots
- JEE Main - 2024
- Mathematics
- Integration
View More Questions
Questions Asked in KCET exam
- The speed of sound in an ideal gas at a given temperature T is v. The rms speed of gas molecules at that temperature is vrms. The ratio of the velocities v and vrms for helium and oxygen gases are X and X' respectively. Then \(\frac{X}{X'}\) is equal to
- KCET - 2023
- Thermodynamics
- If \(p(\frac{1}{q}+\frac{1}{r}),q(\frac{1}{r}+\frac{1}{p}),r(\frac{1}{p}+\frac{1}{q})\) are in A.P., then p, q, r
- KCET - 2023
- Arithmetic Progression
- A stretched wire of a material whose Young's modulus Y = 2 × 1011 Nm-2 has Poisson's ratio of 0.25. Its lateral strain εl = 10-3. The elastic energy density of the wire is
- KCET - 2023
- mechanical properties of solids
- A metallic rod of length 1 m held along east-west direction is allowed to fall down freely. Given horizontal component of earth’s magnetic field BH = 3 × 10-5 T. The emf induced in the rod at an instant t = 2s after it is released is ( Take g = 10 ms-2 )
- KCET - 2023
- Faradays laws of induction
- A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is
- KCET - 2023
- Quantum Physics
View More Questions