Mathematics

# $\displaystyle\int\, \cos\, 2\theta.\,\ln\, \displaystyle \frac {\cos\theta\, +\, \sin\, \theta}{\cos\, \theta\, -\, \sin\, \theta}\, d\theta$

$\, \displaystyle \frac {1}{2}\, \ln\, \left ( \displaystyle \frac {\cos\, \theta\, +\, \sin\, \theta}{\cos\, \theta\, -\, \sin\, \theta} \right )\, \sin\, 2\, \theta\, -\, \displaystyle \frac {1}{2}\, \ln\, (\sec\, 2\,\theta)\, +\, C$

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Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Subjective Hard
Evaluate: $\int\,sin 2 x.cos^{11/2}\,x.(1+cos^{5/2}\,x)^{1/2} dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \int\limits_0^1 {\dfrac{{x{{\tan }^{ - 1}}x}}{{{{\left( {1 + {x^2}} \right)}^{3/2}}}}} dx$ is
• A. $\dfrac{{4 + \pi }}{{4\sqrt 2 }}$
• B. $\dfrac{\pi }{2}$
• C. $- \dfrac{\pi }{2}$
• D. $\dfrac{{4 - \pi }}{{4\sqrt 2 }}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle \int \sqrt{x}(1+x^{1/3})^{4}dx$ is equal to
• A. $\displaystyle 2\left \{ x^{3/2}+\frac{4}{11}x^{11/6}+\frac{6}{13}x^{13/6}+\frac{4}{15}x^{5/2}+\frac{1}{17}x^{17/6} \right \}+c$
• B. $\displaystyle 6\left \{ x^{3/2}-\frac{4}{11}x^{11/6}+\frac{6}{13}x^{13/6}-\frac{4}{15}x^{5/2}+\frac{1}{17}x^{17/6} \right \}+c$
• C. none of these
• D. $\displaystyle 6\left \{ x^{3/2}+\frac{4}{11}x^{11/6}+\frac{6}{13}x^{13/6}+\frac{4}{15}x^{5/2}+\frac{1}{17}x^{17/6} \right \}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following $\displaystyle \underset{1}{\overset{2}{\int}} \dfrac{5x^2}{x^2 + 4x + 3}$

$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$