Mathematics

# Solve:$\int { \tan { x } \tan { 2x } \tan { 3xdx } }$

##### SOLUTION
$\displaystyle\int \tan x\tan 2x\tan 3x dx$.
$\tan 3x=\tan (x+2x)=\dfrac{\tan +\tan 2x}{1-\tan x\tan 2x}$
$\tan 3x(1-\tan x\tan 2x)=\tan x+\tan 2x$
$\tan 3x-\tan x-\tan 2x=\tan x\tan 2x\tan 3x$
$\displaystyle\int \tan 3x-\tan x-\tan 2x dx$
$\Rightarrow \dfrac{1}{3}log|\sec 3x|-\dfrac{1}{2}log|\sec 2x|-log|\sec x|+C$.

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Hard
$\int { \cfrac { dx }{ 2{ x }^{ 2 }+x+3 } } =$?
• A. $\cfrac { 1 }{ \sqrt { 23 } } \tan ^{ -1 }{ \left( \cfrac { 4x+1 }{ \sqrt { 23 } } \right) } +C$
• B. $\cfrac { 1 }{ \sqrt { 23 } } \tan ^{ -1 }{ \left( \cfrac { x+1 }{ \sqrt { 23 } } \right) } +C$
• C. none of these
• D. $\cfrac { 2 }{ \sqrt { 23 } } \tan ^{ -1 }{ \left( \cfrac { 4x+1 }{ \sqrt { 23 } } \right) } +C\quad$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate the integral
$\displaystyle \int_{{\pi }/{6}}^{{\pi }/{3}}\frac{dx}{1+\tan ^{11}x}$
• A. $\displaystyle \frac{\pi }{3}$
• B. $1$
• C. None of the above
• D. $\displaystyle \frac{\pi }{12}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle \frac{dI}{dy}=3^{\cos y}.\sin y$ then $I$ is equal to
• A. $\displaystyle 3^{\cos y}+c$
• B. $\displaystyle \sin y+c$
• C. $3^{\sin y}+c$
• D. $\displaystyle - \dfrac{3^{\cos y}}{\log 3}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\int [1 + \tan x \cdot \tan (x + \alpha)]dx$ is equal to
• A. $\cos \alpha\cdot \log |\dfrac{\sin x}{\sin (x + \alpha)}| + C$
• B. $\tan \alpha\cdot \log |\dfrac{\sin x}{\sin (x + \alpha)}| + C$
• C. $\cot \alpha\cdot \log |\dfrac{\cos (x + \alpha)}{\cos x}| + C$
• D. $\cot \alpha\cdot \log|\dfrac{\sec (x + \alpha)}{\sec x}| + C$

Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.