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\int\frac{x+3}{x^2+4x+5}dx

Integral of (x+3)/(4x+5+x^2)

Answer

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

Step-by-step explanation

Problem

$\int\frac{x+3}{x^2+4x+5}dx$
1

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

$\int\frac{3+x}{-4+4+5+4x+x^2}dx$

Unlock this step-by-step solution!

Answer

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

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$\int\frac{x+3}{x^2+4x+5}dx$

Main topic:

Integration by substitution

Used formulas:

5. See formulas

Time to solve it:

~ 1.19 seconds