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Mathematics
Problem
Evaluate
∫
d
x
(
x
+
3
)
2
+
25
\displaystyle \int \frac{dx}{(x+3)^{2}+25}
∫
(
x
+
3
)
2
+
25
d
x
. a)
1
10
ln
∣
x
+
3
−
5
x
+
3
+
5
∣
+
C
\dfrac{1}{10}\ln\Bigl|\dfrac{x+3-5}{x+3+5}\Bigr|+C
10
1
ln
x
+
3
+
5
x
+
3
−
5
+
C
b)
tan
−
1
x
+
3
5
+
C
\tan^{-1}\dfrac{x+3}{5}+C
tan
−
1
5
x
+
3
+
C
c)
1
5
tan
−
1
x
+
3
5
+
C
\dfrac{1}{5}\tan^{-1}\dfrac{x+3}{5}+C
5
1
tan
−
1
5
x
+
3
+
C
d)
1
5
cot
−
1
x
+
3
5
+
C
\dfrac{1}{5}\cot^{-1}\dfrac{x+3}{5}+C
5
1
cot
−
1
5
x
+
3
+
C
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