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CBSE
MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals
Problem
Find
∫
x
2
+
3
x
+
5
x
+
1
d
x
\displaystyle\int \frac{x^{2}+3x+5}{x+1}\,dx
∫
x
+
1
x
2
+
3
x
+
5
d
x
. (a)
1
2
x
2
+
2
x
+
ln
∣
x
+
1
∣
+
C
\dfrac12 x^{2}+2x+\ln|x+1|+C
2
1
x
2
+
2
x
+
ln
∣
x
+
1∣
+
C
(b)
1
2
x
2
+
2
x
+
3
ln
∣
x
+
1
∣
+
C
\dfrac12 x^{2}+2x+3\ln|x+1|+C
2
1
x
2
+
2
x
+
3
ln
∣
x
+
1∣
+
C
(c)
1
2
x
2
+
2
x
+
3
ln
∣
x
∣
+
C
\dfrac12 x^{2}+2x+3\ln|x|+C
2
1
x
2
+
2
x
+
3
ln
∣
x
∣
+
C
(d)
x
2
+
2
x
+
3
ln
∣
x
+
1
∣
+
C
x^{2}+2x+3\ln|x+1|+C
x
2
+
2
x
+
3
ln
∣
x
+
1∣
+
C
Related theory
Integration Techniques
Integration by partial fractions
Integrals
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