Evaluate the integral. \int \frac{dx}{x^{2}+2x+10}

BolkowN

BolkowN

Answered question

2021-11-09

Evaluate the integral.
dxx2+2x+10

Answer & Explanation

likvau

likvau

Skilled2021-11-10Added 75 answers

Given,
dxx2+2x+10
Now consider,
x2=2x+10=x2+2x+1+9
=(x+1)2+32
Therefore given integral becomes,
dxx2+2x+10=dx(x+1)2+32
=13tan1(x+13)+C   [dxx2+a2=1atan1(xa)+C]

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