Mathematics

# Evaluate$\displaystyle \int \dfrac {x+2}{\sqrt {x^{2}+4x+1}}.dx$

##### SOLUTION
We have,
$I=\displaystyle \int \dfrac {x+2}{\sqrt {x^{2}+4x+1}}dx$

Let
$t=x^2+4x+1$
$\dfrac{dt}{dx}=2x+4$
$\dfrac{dt}{2}=(x+2)dx$

Therefore,
$I=\dfrac{1}{2}\displaystyle \int \dfrac {1}{\sqrt {t}}dt$
$I=\dfrac{1}{2}(2\sqrt t)+C$
$I=\sqrt t+C$

On putting the value of $t$, we get
$I=\sqrt {x^2+4x+1}+C$

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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
If $\displaystyle I=\int { \left( \sqrt { \tan { x } } +\sqrt { \cot { x } } \right) } dx=f\left( x \right)+c$
• A. $\sqrt { 2 } \sin ^{ 1 }\times \left( \sin { x } -\cos { x } \right)$
• B. $\sqrt { 2 } \sin ^{ 1- }\times \left( \sin { x } +\cos { x } \right)$
• C. $none\ of these$
• D. $\sqrt { 2 } \sin ^{ -1 }\times \left( \sin { x } -\cos { x } \right)$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following integral:
$\displaystyle\int^a_0\dfrac{x}{\sqrt{a^2+x^2}}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve:-
$\displaystyle \int \dfrac{e\ log\ x}{x}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $I_n = \int_0^{\pi /4}\tan^n dx ,$ then $\dfrac {1}{I_2 + I_4} \dfrac {1}{I_3 + I_5} \dfrac {1}{I_4 + I_6}$ is :
• A. G.P.
• B. H.P.
• C. None of these
• D. A.P.

$\int {\dfrac{{\left( {1 + \cot \,x} \right)}}{{\left( {x + \,\log \,\sin \,x} \right)}}\,dx} =?$