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 Complete the square and find xx2+10x+30dx\text { Complete the square and find } \int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x \text {. }

Question 13

Multiple Choice

 Complete the square and find xx2+10x+30dx\text { Complete the square and find } \int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x \text {. }


A) xx2+10x+30dx=x2+10x+305lnx2+10x+30+(x+5) +C\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \sqrt { x ^ { 2 } + 10 x + 30 } - 5 \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } + ( x + 5 ) \right| + C
B) xx2+10x+30dx=x2+10x+30+lnx2+10x+30+(x+5) +C\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \sqrt { x ^ { 2 } + 10 x + 30 } + \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } + ( x + 5 ) \right| + C
C) xx2+10x+30dx=lnx2+10x+30+C\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } \right| + C
D) xx2+10x+30dx=5lnx2+10x+30+(x+5) +C\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = 5 \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } + ( x + 5 ) \right| + C
E) xx2+10x+30dx=x2+10x+305lnx2+10x+30+C\int \frac { x } { \sqrt { x ^ { 2 } + 10 x + 30 } } d x = \sqrt { x ^ { 2 } + 10 x + 30 } - 5 \ln \left| \sqrt { x ^ { 2 } + 10 x + 30 } \right| + C

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