Mathematics

# Evaluate $\int \dfrac {1}{\sqrt {7-6x-{x}^{2}}}$

##### SOLUTION
$\int {\cfrac{1}{{\sqrt {7 - 6x - {x^2}} }}dx}$
$\int {\cfrac{1}{{\sqrt { - {x^2} - 6x + 7} }}}$
$\int {\cfrac{{dx}}{{\sqrt { - \left( {{x^2} + 6x - 7} \right)} }}}$
$\int {\cfrac{{dx}}{{\sqrt { - 1\left[ {{x^2} + 6x + 9 - 9 - 7} \right]} }}}$
$\int {\cfrac{{dx}}{{\sqrt { - 1\left[ {{{\left( {x + 3} \right)}^2} - 16} \right]} }}}$
$\int {\cfrac{{dx}}{{\sqrt {{{\left( 4 \right)}^2} - {{\left( {x + 3} \right)}^2}} }}}$
$={\sin ^{ - 1}}\left( {\cfrac{{x + 3}}{4}} \right) + c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Subjective Medium
Solve:
$\int {\sqrt {{(x- 2)} {(x - 2)} } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int e^{x}(x^{2}-5x+8)$ dx $=e^{x}f(x)+c$ then $f(x)$
• A. $x^{2}-5x+12$
• B. $x^{2}+7x+15$
• C. $x^{2}-7x-15$
• D. $x^{2}-7x+15$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve : $\underset{0}{\overset{\pi}{\displaystyle\int}} \pi \, \sin^3 \, x \, dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\int \frac { x ^ { 2 } \tan ^ { - 1 } x } { 1 + x ^ { 2 } } d x = \tan ^ { - 1 } x - \frac { 1 } { 2 } \log \left( 1 + x ^ { 2 } \right) + f ( x ) + c$ then $f ( x ) =$
• A. $- \frac { \tan ^ { - 1 } x } { 2 }$
• B. $\frac { \tan ^ { - 1 } x } { 2 }$
• C. None of these
• D. $- \frac { 1 } { 2 } \left( \tan ^ { - 1 } x \right) ^ { 2 }$

$\int {\cos e{c^2}x} \log \sec x\,dx$