Mathematics

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


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Subjective Medium Published on 17th 09, 2020
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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. $$-\displaystyle \dfrac{1}{\sqrt{5}}cosh^{-1}\dfrac{7+4x}{3(2x+1)}+c$$
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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. $$\log\left|\log\left(\cot \dfrac {x}{2}\right)\right|+c$$
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1 Verified Answer | Published on 17th 09, 2020

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Q3 Single Correct Hard
Evaluate $$\displaystyle \int \frac{3\sin x+2\cos x}{3\cos x+2\sin x}dx.$$
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  • C. None of these
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Q4 Subjective Medium
$$\displaystyle\int_{0}^{2} 3x+2\ dx$$

Asked in: Mathematics - Integrals


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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

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