Mathematics

# The value of $\displaystyle \int \dfrac {3x+5}{3x^2+10x+6} \ dx$ is

##### SOLUTION
Let
$3x^2+10x+6=t$

$6x+10dx=dt$...........$(differentiating \ with \ respect \ to \ x)$

$2(3x+5)=\dfrac {dt} {dx}$

$\displaystyle \int \dfrac 12 \cdot \dfrac 1tdt$

$=\dfrac 12\log t+c$

$=\dfrac 12\log(3x^2+10x+6)+c$

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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
$\left[ \int \log ( 1 + \cos x ) - x \tan \frac { x } { 2 } \right] d x$ is equal to ?
• A. $x \tan \frac { x } { 2 }$
• B. $x \log ( 1 + \cos x )$
• C. None of these
• D. $\log ( 1 + \cos x )$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
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Q3 TRUE/FALSE Medium
State true or false:
The value of the integral $\displaystyle \int_{-\infty }^{0}x.e^{x}dx$ is not finite.
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• B. False

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
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Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
Case I If $m>0$, then put $\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$
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Case III If quadratic equation $mx^2+nx+p=0$ has real roots $\alpha$ and $\beta$, then put $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$