Mathematics

# Evaluate: $\displaystyle\int {\frac{{1 - \cot x}}{{1 + \cot x}}dx}$

##### SOLUTION
$I=\displaystyle\int \dfrac{1-\cot x}{1+\cot x}dx$

$\Rightarrow \displaystyle\int \dfrac{1-\dfrac{\cos x}{\sin x}}{1+\dfrac{\cos x}{\sin x}}dx$

$\Rightarrow \displaystyle\int \dfrac{\sin x-\cos x}{\sin x+\cos x}dx$

$\sin x+\cos x=t$

$(\cos x-\sin x)dx=dt$

$=\displaystyle\int -\dfrac{dt}{t}$

$=-ln |t|+c$

$=-ln|\sin x+\cos x|+c$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Hard
$\int \tan^{3} 2x \sec 2x dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Assertion & Reason Hard
##### ASSERTION

$\displaystyle \int{\sqrt{x-\sqrt{x^{2}-4}}} dx\displaystyle =\left [ \frac{1}{3}\left ( \sqrt{x+2}-\sqrt{x-2} \right )^{3} +2\left ( \sqrt{x+2}+\sqrt{x-2} \right )\right ]+C$

##### REASON

The integral in assertion can be computed by substituting $\displaystyle \left ( \sqrt{x+2}-\sqrt{x-2} \right )^{2}=2t.$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Solve $\left[-\displaystyle \int^{\pi/2}_0\cos \left(\dfrac{\pi}{4}+\dfrac{x}{2}\right)e^x\right]dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve :
$\displaystyle \int x \sqrt{x-1 dx}$

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