Mathematics

Evaluate $$\displaystyle\int \dfrac {e^{x}(1+x)}{\sin^{2}(xe^{x})}dx$$


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Subjective Medium Published on 17th 09, 2020
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Q1 Single Correct Medium
The value of $$\int \sqrt{\dfrac{1 - \sqrt{2}}{1 + \sqrt{x}}} dx$$ is equal to :
  • A. $$-2 \sqrt{1 - x} + cos^{-1} \, \sqrt{x} + \sqrt{x (1 - x)} + c$$
  • B. $$-2 \sqrt{1 + x} + cos^{-1} \, \sqrt{x} + \sqrt{x (1 - x)} + c$$
  • C. none of these
  • D. $$-2 \sqrt{1 - x} + cos^{-1} \, \sqrt{x} + \sqrt{1 - x + c}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Single Correct Medium
$$\displaystyle \int_{0}^{\infty} \dfrac {x \ln x}{(1 + x^{2})^{2}}dx =$$
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  • B. $$-1$$
  • C. $$\dfrac {\pi}{2}$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Evaluate : $$\int \dfrac { 1 } { ( x + 1 ) \sqrt { 3 + 2 x - x } } d x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Single Correct Hard
The value of $$\smallint {\textstyle{1 \over {x + \sqrt {x - 1} }}}$$ dx is 
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  • C. none of these
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Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Subjective Medium
$$\displaystyle\int^0_{-2}(x^3+3x^2+3x+(x+1)\cos(x+1)dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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