Question

evaluate to 1.dp
integral of 3 and 1 for 2/2x+5 dx

Answer 1

This is a simple application of the natural logarithm. Give it a go.

Answer 2

i obviously have lol

Answer 3

Not a helpful answer. \(\int \dfrac{1}{x}\;dx = \ln|x| + C\)

Utilize this result.

Answer 4

Try a u substitution -

let u = 2x + 1
then \[\frac{du}{dx} = 2\]so\[\frac{ du }{ 2} = dx\]
Now put them into the integral, and change the limits.
\[\large \int\limits_{1}^{3} \frac{ 2 }{ 2x+5 } dx = \int\limits_{a}^{b} \frac{ 2 }{u } \frac{ du }{2 }\]

Answer 5

To change the limits, put the old limits (x=1 and x=3) into the equation for u:

u = 2x+1

To find the limits for u.