Mathematics

$$\int { \left( { e }^{ ln\quad sinx }-cos\quad x \right)  } $$ dx is equal to :


ANSWER

$$ sin x-x cosx +c $$


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Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
If $$I_{1}=\displaystyle \int_{e}^{e^{2}}\dfrac{dx}{\ell n x}$$ and $$I_{2}=\int_{1}^{2} \dfrac{e^{x}}{x}dx$$, then 
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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 $$\displaystyle \left ( \sqrt{x+2}-\sqrt{x-2} \right )^{2}=2t.$$

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