Final answer to the problem
$4.6931472$
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Step-by-step Solution
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1
Expand the fraction $\frac{2t+3}{t+1}$ into $2$ simpler fractions with common denominator $t+1$
$\int_{1}^{3}\left(\frac{2t}{t+1}+\frac{3}{t+1}\right)dt$
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$\int_{1}^{3}\left(\frac{2t}{t+1}+\frac{3}{t+1}\right)dt$
Learn how to solve definite integrals problems step by step online. Integrate the function (2t+3)/(t+1) from 1 to 3. Expand the fraction \frac{2t+3}{t+1} into 2 simpler fractions with common denominator t+1. Simplify the expression inside the integral. The integral 2\int_{1}^{3}\frac{t}{t+1}dt results in: 2.6137056. The integral \int_{1}^{3}\frac{3}{t+1}dt results in: \ln\left(8\right).
Final answer to the problem
$4.6931472$