Mathematics

# Evaluate: $\displaystyle \int \dfrac {2x}{x^2} dx$

##### SOLUTION
$I=\displaystyle \int \dfrac {2x}{x^2} dx$

$I=\displaystyle \int \dfrac 2xdx$

$I=2\log xdx$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate  $\int _{ 0 }^{ 1 }{ \sqrt { \cfrac { x }{ 1-{ x }^{ 3 } } } } dx=$
• A. $\cfrac{\pi}{4}$
• B. $\cfrac{\pi}{3}$
• C. $\cfrac{\pi}{6}$
• D. $\cfrac{\pi}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle\int_{0}^{2}x\sqrt{x+2} \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int { { x }^{ 4 }{ e }^{ 2x } } dx=$
• A. $\cfrac { { e }^{ 2x } }{ 2 } \left( 2{ x }^{ 4 }-4{ x }^{ 3 }+6{ x }^{ 2 }-6x+3 \right) +C$
• B. $\cfrac { { e }^{ 2x } }{ 8 } \left( 2{ x }^{ 4 }+4{ x }^{ 3 }+6{ x }^{ 2 }+6x+3 \right) +C$
• C. $\cfrac { { e }^{ 2x } }{ 4 } \left( 2{ x }^{ 4 }+4{ x }^{ 3 }+6{ x }^{ 2 }+6x+3 \right) +C$
• D. $\cfrac { { e }^{ 2x } }{ 4 } \left( 2{ x }^{ 4 }-4{ x }^{ 3 }+6{ x }^{ 2 }-6x+3 \right) +C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following:
$\displaystyle \int_{0}^{\dfrac{1}{2}} \dfrac{dx}{(1 + x^2) \sqrt{1 - x^2}}$ (Hint: let $x = sin \,\theta$)

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$