Mathematics

# Evaluate : $\displaystyle \int \frac{2x+3}{x^2+3x-18}dx$

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

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \int\dfrac{1}{(2x+1)\sqrt{x^{2}-x-2}}dx=$
• A. $-\displaystyle \dfrac{1}{\sqrt{5}} cos \displaystyle \dfrac{7+4x}{3(2x+1)}+c$
• B. $-\dfrac{1}{\sqrt{5}}sinh^{-1}\dfrac{7+4x}{3(2x+1)}+c$
• C. $-\displaystyle \dfrac{1}{\sqrt{5}}cosh^{-1}\dfrac{7+4x}{3(2x+1)}+c$
• D. $-\dfrac{1}{\sqrt{5}}\sin^{-1}\dfrac{7+4x}{3(2x+1)}+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate: $\displaystyle \int\frac{co\sec x}{\log|\tan\frac{x}{2}|}d{x}$
• A. ${-}\displaystyle \log\left|\log\left(\tan\dfrac{x}{2}\right)\right|+c$
• B. $\log\left|\log\left(\cot \dfrac {x}{2}\right)\right|+c$
• C. $-\log\left|\log\left(\cot \dfrac {x}{2}\right)\right|+c$
• D. $\displaystyle \log\left|\log\left(\tan\dfrac{x}{2}\right)\right|+c$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate $\displaystyle \int \frac{3\sin x+2\cos x}{3\cos x+2\sin x}dx.$
• A. $\displaystyle \frac{12}{13}x+\displaystyle \frac{-5}{13}\log \left | 2\cos x-3\sin x \right |+C$
• B. $\displaystyle \frac{-5}{13}x+\displaystyle \frac{12}{13}\log \left | 3\cos x-2\sin x \right |+C$
• C. None of these
• D. $\displaystyle \frac{12}{13}x+\displaystyle \frac{-5}{13}\log \left | 3\cos x+2\sin x \right |+C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\displaystyle\int_{0}^{2} 3x+2\ dx$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$

Then answer the following question.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020