Mathematics

# Evaluate  $\int\limits_0^1 {\dfrac{{2x}}{{5{x^2} + 1}}dx}$

##### SOLUTION
$\displaystyle \int_0^1\dfrac{2x}{5x^2+1}dx$
$x^2=t$    $2xdx=dt$
$\displaystyle \int_0^1\dfrac{dt}{st+1}$
$\left[\dfrac{1}{5}\log |5t+1|\right]^1_0$
$\left[\dfrac{1}{5}\log|5x^2+1|\right]^1_0$
$\dfrac{1}{5}\log 6$

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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 Hard
$\displaystyle\int_{0}^{a}x^{4}\left ( a^{2}-x^{2} \right )^{1/2} dx$ equals
• A. $\displaystyle\frac{\pi a^{5}}{32}$
• B. $\displaystyle \frac{\pi a^{2}}{32}$
• C. None of these
• D. $\displaystyle\frac{\pi a^{6}}{32}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate : $\displaystyle \int _{ 0 }^{ \log _{ e }{ 5 } }{ \dfrac { { e }^{ x }\sqrt { { e }^{ x }-1 } }{ { e }^{ x }+3 } dx }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle \int{\cos^{2}x\, dx}$.

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Integrate the following function with respect to x
$\displaystyle \int \left ( 5x^{2}+3x-2 \right )dx$

• A. $\displaystyle \frac{5x^{3}}{3}-\frac{3x^{3}}{2}-2x+c$
• B. $\displaystyle \frac{5x^{3}}{3}-\frac{3x^{2}}{2}+2x-c$
• C. $\displaystyle \frac{5x^{3}}{3}+\frac{3x^{3}}{2}+2x+c$
• D. $\displaystyle \frac{5x^{3}}{3}+\frac{3x^{2}}{2}-2x+c$

Solve $\int {{{\left( {2x + 3} \right)}^2}dx}$