Mathematics

# Evaluate $\displaystyle \int {\frac{{dx}}{{x + 4 - {x^2}}}}$

##### SOLUTION
$\displaystyle \int { \dfrac { dx }{ x+4-{ x }^{ 2 } } } =-\int { \dfrac { dx }{ { x }^{ 2 }-x-4 } }$
$=\displaystyle \int { \dfrac { -dx }{ { \left( x-\dfrac { 1 }{ 2 } \right) }^{ 2 }-4-\dfrac { 1 }{ 4 } } }$
$=\displaystyle \int { \dfrac { -dx }{ { \left( x-\dfrac { 1 }{ 2 } \right) }^{ 2 }-{ \left( \dfrac { \sqrt { 17 } }{ 2 } \right) }^{ 2 } } }$
$=\dfrac { -1 }{ \sqrt { 17 } } ln\left( \dfrac { x-\dfrac { 1 }{ 2 } -\dfrac { \sqrt { 17 } }{ 2 } }{ x-\dfrac { 1 }{ 2 } +\dfrac { \sqrt { 17 } }{ 2 } } \right) +c$
$=\dfrac { -1 }{ \sqrt { 17 } } ln\left( \dfrac { 2x-1-\sqrt { 17 } }{ 2x-1+\sqrt { 17 } } \right) +c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

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