Mathematics

# If $\displaystyle\int { { x }^{ 1-/2 }{ \left( 2+{ 3x }^{ 1/3 } \right) }^{ -2 } } dx=$$A\tan ^{ -1 }{ \left\{ \sqrt { \dfrac { 3 }{ 2 } } { x }^{ 1/6 } \right\} } +B\dfrac { { x }^{ 1/6 } }{ 2+{ 3x }^{ 1/3 } } +C$ then

$A=\dfrac{1}{\sqrt{6}}$

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

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle \int \dfrac{dx}{x(x^2+1)}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
The value of $\displaystyle\int\limits_{-1}^{1}\sin ^{11}x.\cos^{12}x\ dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle \int \dfrac {x^2+1}{\sqrt {x^2 +2} }dx$ is equal to:
• A. $\sqrt {({x^2} + 2)} + C$
• B. $2\sqrt {({x^2} + 2)} + C$
• C. $x\sqrt {({x^2} + 2)} + C$
• D. $\dfrac{x\sqrt {({x^2} + 2)}}{2} + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find :
$\displaystyle\int {\dfrac{2}{(1-x)(1+x^2)}dx}$

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 $(0, 1)$