Evaluate the following integral. ∫2x3−11x2+2x−16(x2−4)(x2+1)dx

abreviatsjw

abreviatsjw

Answered

2022-01-17

Evaluate the following integral.
2x311x2+2x16(x24)(x2+1)dx

Answer & Explanation

macalpinee3

macalpinee3

Expert

2022-01-18Added 29 answers

Step 1
Evaluate
2x311x2+2x16(x24)(x2+1)dx
Step 2
Simplify the denominator by factorization.
2x311x2+2x16(x+2)(x2)(x2+1)dx
Step 3
Now simplify by partial fraction decomposition we get
(1x2+1+4x+22x2)dx
=1x2+1dx+4x+2dx2x2dx
Step 4
Now integrating we get
1x2+1dx+41x+2dx21x2dx
=tan1(x)+4ln(x+2)2ln(x2)+c
Step 5
ANSWER
2x311x2+2x16(x24)(x2+1)dx=tan1(x)+4ln(x+2)2ln(x2)+c

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