Mathematics

# Solve:$\int\frac{1}{{1 + {x^2}}}$ dx

##### SOLUTION
$I=\displaystyle \int \dfrac {dx}{1+x^2}$
put
$x=\tan p$
$dx=\sec^2p \ dp$
$dx=(1+\tan^2 p)dp$
$dx=(1+x^2)dp$
$\Rightarrow \ \dfrac {dx}{(1+x^2)}=dp$
$I=\displaystyle \int dp\quad =p+c=\tan^{-1}x+c$
$\therefore \ \displaystyle \int \dfrac {dx}{1+x^2}=\tan^{-1}x+c$

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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
$\displaystyle \frac{1}{x^{4}+1}=$
• A. $[\displaystyle \frac{x+\sqrt{2}}{2\sqrt{2}\sqrt{2}}\frac{x+\sqrt{2}}{2\sqrt{2}(x^{2}-\sqrt{2}x+1)}]$
• B. $[\displaystyle \frac{x+\sqrt{2}}{x^{2}+\sqrt{2}x+1}-\frac{x+\sqrt{2}}{(x^{2}-\sqrt{2}x+1)}]$
• C. $[\displaystyle \frac{x+\sqrt{2}}{2\sqrt{2}(x^{2}+\sqrt{2}x+1)}\frac{\sqrt{2}-x}{(-\sqrt{2})}]$
• D. $\displaystyle \frac{1}{2\sqrt{2}}[\frac{\mathrm{x}+\sqrt{2}}{(\mathrm{x}^{2}+\sqrt{2}\mathrm{x}+1)}+\frac{\sqrt{2}-\mathrm{x}}{(\mathrm{x}^{2}-\sqrt{2}\mathrm{x}+1)}]$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\alpha > 1$, then $\int \dfrac {dx}{x^{2} + 2\alpha x + 1} =$.
• A. $\dfrac {1}{\sqrt {1 - \alpha^{2}}}\cot^{-1} \left (\dfrac {x + \alpha}{\sqrt {1 - \alpha^{2}}}\right ) + c$
• B. $\dfrac {1}{2\sqrt {\alpha^{2} - 1}}\log \left (\dfrac {x + \alpha - \sqrt {\alpha^{2} - 1}}{x + \alpha + \sqrt {\alpha^{2} - 1}}\right ) + c$
• C. $\dfrac {1}{2\sqrt {\alpha^{2} - 1}}\log \left (\dfrac {x + \alpha + \sqrt {\alpha^{2} - 1}}{x + \alpha - \sqrt {\alpha^{2} - 1}}\right ) + c$
• D. $\dfrac {1}{\sqrt {1 - \alpha^{2}}}\tan^{-1} \left (\dfrac {x + \alpha}{\sqrt {1 - \alpha^{2}}}\right ) + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\displaystyle\int_{}^{} {\dfrac{{1 - \frac{1}{{{x^2}}}}}{{{x^2} + \frac{1}{{{x^2}}} + 3}}} dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve : $\displaystyle \int \dfrac{x \, dx }{(x^2 + a^2) (x^2 + b^2)}$

Solve $\displaystyle\int\limits_0^x {\dfrac{{\sqrt x }}{{\sqrt x + \sqrt {8 - x} }}dx}$