Evaluate the integral.
-$$\int \frac { d x } { x ^ { 2 } + 6 x + 25 }$$
A) $\frac { 1 } { 4 } \tan ^ { - 1 } \left( \frac { \mathrm { x } + 3 } { 4 } \right) + \mathrm { C }$
B) $\frac { 1 } { 4 } \sin ^ { - 1 } \left( \frac { x + 3 } { 4 } \right) + C$
C) $( 2 x + 6 ) \ln \left| x ^ { 2 } + 6 x + 25 \right| + C$
D) $4 \tan ^ { - 1 } \left( \frac { \mathrm { x } + 3 } { 4 } \right) + \mathrm { C }$

Question

Quizplus · Accepted Answer

The integral can be solved by completing the square in the denominator to get $x^2 + 6x + 25 = (x+3)^2 + 16$. Then, using the substitution $u = \frac{x+3}{4}$, the integral becomes $\frac{1}{4} \tan^{-1}(u) + C$, which matches choice A.

Evaluate the Integral ∫dxx2+6x+25\int \frac { d x } { x ^ { 2 } + 6 x + 25 }∫x2+6x+25dx​

Evaluate the Integral $\int \frac { d x } { x ^ { 2 } + 6 x + 25 }$