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Step-by-step Solution

Integral of 1/(x^2+10x+29)

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Answer

$\frac{1}{4}2arctan\left(\frac{1}{2}\left(x+5\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\:\frac{dx}{x^2+10x+29}$
1

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$\int\frac{1}{x^2+10x+29+25-25}dx$
2

Factor the perfect square trinomial $x^2+10x+25$

$\int\frac{1}{\left(x+5\right)^2+4}dx$

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Answer

$\frac{1}{4}2arctan\left(\frac{1}{2}\left(x+5\right)\right)+C_0$
$\int\:\frac{dx}{x^2+10x+29}$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 0.69 seconds