Question

4) I = (5x+2)dx/(x²+4)​

Answer 1

Step-by-step explanation:

We have,

$\int \limits ^{2} _{0} \frac{5x + 2}{ {x}^{2} + 4} dx$

$= \frac{5}{2} \int \limits ^{2} _{0} \frac{2x }{ {x}^{2} + 4} dx + 2\int \limits ^{2} _{0} \frac{dx}{ {x}^{2} + 4}$

$= \frac{5}{2} [ ln( {x}^{2} + 4 ) ] ^{2}_{0} + 2 [\tan ^{ - 1} ( \frac{x}{2} ) ] ^{2} _{0}$

$= \frac{5}{2} ( ln(8) - ln(4) ) + 2( \tan^{ - 1} (1) - \tan^{ - 1} (0))$

$= \frac{5}{2} ln(2) + \frac{\pi}{2}$