Mathematics

# Evaluate $\displaystyle\int \dfrac {3x}{2x^2+5}dx$

##### SOLUTION
$\displaystyle \int \dfrac{3x}{2x^2+5}dx\\t=2x^2+5\implies 4xdx=dt\\\displaystyle \int \dfrac 34 \dfrac 1t dt\\\dfrac 34\log t\\\dfrac 34\log (2x^2+5)+c$

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate: $\int\limits_1^2 {\dfrac{1}{{{x^2}}}{e^{\tfrac{{ - 1}}{x}}}dx = }$
• A. $\dfrac{{e - 1}}{e}$
• B. $\dfrac{{e - 1}}{{\sqrt e }}$
• C. $\dfrac{{1 - e}}{{\sqrt e }}$
• D. $\dfrac{{\sqrt e - 1}}{e}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate $\displaystyle \int_{a}^{b}x\ dx$

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Q3 Subjective Medium
Solve:
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Q4 Subjective Hard
Evaluate
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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 $\displaystyle f(x)>0 \forall x \in R$