Mathematics

# Find  $\int { \dfrac { ({ x }^{ 2 }+1)({ { x }^{ 2 } }+2) }{ ({ { x }^{ 2 } }+3)({ { x }^{ 2 } }+4) } dx }$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Hard
Evaluate:
$\displaystyle \int { \cfrac { { x }^{ 2 } }{ { x }^{ 4 }-{ x }^{ 2 }-12 } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Suppose f, f' and f'' are continuous on [0,e] and that f'(e)=f(e)=f(1)=1and $\displaystyle \int_{1}^{e}\frac{f\left ( x \right )}{x^{2}}dx=\frac{1}{2}$ then the value of $\displaystyle \int_{1}^{e}f''\left ( x \right )lnxdx$ equals
• A.
• B. 1
• C. 2
• D. none of these

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integral:
$\int { \cfrac { \sin { \left( 2+3\log { x } \right) } }{ x } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
$\int { \tan ^{ -1 }{ \left( \sqrt { x } \right) } } dx$

Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$