Question

$\int_{}^{}\frac{dx}{2x^{2} + x + 1}$ equals :

• A. $\frac{2}{\sqrt{7}}\tan^{- 1}\left( \frac{4x + 1}{\sqrt{7}} \right) + C$
• B. $\frac{1}{2\sqrt{7}}\tan^{- 1}\left( \frac{4x + 1}{\sqrt{7}} \right) + C$
• C. $\frac{1}{2}\tan^{- 1}\left( \frac{4x + 1}{\sqrt{7}} \right) + C$
• D. None

Answer 1

Answer: (A)

$\frac{2}{\sqrt{7}}\tan^{- 1}\left( \frac{4x + 1}{\sqrt{7}} \right) + C$

Answer 2

I = $\frac { 1 } { 2 }$

I = $\frac { 1 } { 2 }$ $\int \frac { d x } { \left( x + \frac { 1 } { 4 } \right) ^ { 2 } + \left( \frac { \sqrt { 7 } } { 4 } \right) ^ { 2 } }$

I = $\frac { 1 \times 4 } { 2 \times \sqrt { 7 } }$ tan^–1$\left( \frac { x + \frac { 1 } { 4 } } { \frac { \sqrt { 7 } } { 4 } } \right)$ + C

I = $\frac { 2 } { \sqrt { 7 } }$ tan^–1$\left( \frac { 4 x + 1 } { \sqrt { 7 } } \right)$+ C