Final answer to the problem
$2\ln\left|x-1\right|+3\ln\left|x+3\right|+C_0$
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1
Rewrite the expression $\frac{5x+3}{x^2+2x-3}$ inside the integral in factored form
$\int\frac{5x+3}{\left(x-1\right)\left(x+3\right)}dx$
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$\int\frac{5x+3}{\left(x-1\right)\left(x+3\right)}dx$
Learn how to solve problems step by step online. int((5x+3)/(x^2+2x+-3))dx. Rewrite the expression \frac{5x+3}{x^2+2x-3} inside the integral in factored form. Rewrite the fraction \frac{5x+3}{\left(x-1\right)\left(x+3\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{2}{x-1}+\frac{3}{x+3}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{2}{x-1}dx results in: 2\ln\left(x-1\right).
Final answer to the problem
$2\ln\left|x-1\right|+3\ln\left|x+3\right|+C_0$
