Mathematics

# The value of $\displaystyle \int \dfrac {x^2+1}{\sqrt {x^2 +2} }dx$ is equal to:

$\dfrac{x\sqrt {({x^2} + 2)}}{2} + C$

##### SOLUTION
Now,
$\displaystyle \int \dfrac {x^2+1}{\sqrt {x^2+2} }dx$

$=\displaystyle \int \dfrac {x^2+2-1}{\sqrt {x^2+2} }dx$

$=\displaystyle\int{\sqrt {x^2+2} }dx$$-\displaystyle \int \dfrac {1}{\sqrt {x^2+2} }dx$

$=\dfrac{x\sqrt{x^2+2}}{2}+\dfrac{2}{2}\log\left |x+\sqrt{x^2+2}\right|-\log\left|x+\sqrt{x^2+2}\right|+c$ [ Where $c$ is integrating constant]

$=\dfrac{x\sqrt{x^2+2}}{2}+c$.

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle \int \frac{{x{e^x}}}{{{{\left( {1 + x} \right)}^2}}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int { \frac { dx }{ x\left( { x }^{ 7 }+1 \right) } } \\$ is equal to:
• A. $\displaystyle \log { \left( \frac { { x }^{ 7 } }{ { x }^{ 7 }+1 } \right) }$
• B. $\displaystyle \log { \left( \frac { { x }^{ 7 }+1 }{ { x }^{ 7 } } \right) } +c$
• C. $\displaystyle \frac { 1 }{ 7 } \log { \left( \frac { { x }^{ 7 }+1 }{ { x }^{ 7 } } \right) } +c$
• D. $\displaystyle \frac { 1 }{ 7 } \log { \left( \frac { { x }^{ 7 } }{ { x }^{ 7 }+1 } \right) } +c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle \int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve :
$\displaystyle \int_0^{\pi}\dfrac{1}{a^2-2a \cos x+1}dx$

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 $\displaystyle f(x)>0 \forall x \in R$