Final Answer
$-\frac{1}{2}\ln\left(s+1\right)+\frac{s}{2\left(s^2+1\right)}+\frac{1}{-2\left(s^2+1\right)}+\frac{1}{4}\ln\left(s^2+1\right)+C_0$
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Step-by-step Solution
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1
Take out the constant $2$ from the integral
$2\int\frac{s}{\left(s+1\right)\left(s^2+1\right)^2}ds$
Learn how to solve simplify trigonometric expressions problems step by step online.
$2\int\frac{s}{\left(s+1\right)\left(s^2+1\right)^2}ds$
Learn how to solve simplify trigonometric expressions problems step by step online. Find the integral int((2s)/((s+1)(s^2+1)^2))ds. Take out the constant 2 from the integral. Rewrite the fraction \frac{s}{\left(s+1\right)\left(s^2+1\right)^2} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D, F. The first step is to multiply both sides of the equation from the previous step by \left(s+1\right)\left(s^2+1\right)^2. Multiplying polynomials.
Final Answer
$-\frac{1}{2}\ln\left(s+1\right)+\frac{s}{2\left(s^2+1\right)}+\frac{1}{-2\left(s^2+1\right)}+\frac{1}{4}\ln\left(s^2+1\right)+C_0$