Final Answer
$\ln\left(s\right)-\frac{5}{\sqrt{15}}\ln\left(\frac{8.872983+s}{\sqrt{-15+\left(s+5\right)^2}}\right)+\ln\left(\frac{\sqrt{15}}{\sqrt{-15+\left(s+5\right)^2}}\right)+C_0$
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Step-by-step Solution
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1
Rewrite the fraction $\frac{10s+10}{s\left(s^2+10s+10\right)}$ in $2$ simpler fractions using partial fraction decomposition
$\frac{10s+10}{s\left(s^2+10s+10\right)}=\frac{A}{s}+\frac{Bs+C}{s^2+10s+10}$
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$\frac{10s+10}{s\left(s^2+10s+10\right)}=\frac{A}{s}+\frac{Bs+C}{s^2+10s+10}$
Learn how to solve problems step by step online. Find the integral int((10s+10)/(s(s^2+10s+10)))ds. Rewrite the fraction \frac{10s+10}{s\left(s^2+10s+10\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by s\left(s^2+10s+10\right). Multiplying polynomials. Simplifying.
Final Answer
$\ln\left(s\right)-\frac{5}{\sqrt{15}}\ln\left(\frac{8.872983+s}{\sqrt{-15+\left(s+5\right)^2}}\right)+\ln\left(\frac{\sqrt{15}}{\sqrt{-15+\left(s+5\right)^2}}\right)+C_0$