Question

2v+5 / v+2 dv ka integration

Answer 1

SOLUTION

TO EVALUATE

$\displaystyle \sf{\int\limits_{}^{} \frac{2v + 5}{v + 2} \, dv }$

EVALUATION

Here the given Integral is

$\displaystyle \sf{\int\limits_{}^{} \frac{2v + 5}{v + 2} \, dv }$

We integrate as below

$\displaystyle \sf{\int\limits_{}^{} \frac{2v + 5}{v + 2} \, dv }$

$\displaystyle \sf{ = \int\limits_{}^{} \frac{2v + 4 + 1}{v + 2} \, dv }$

$\displaystyle \sf{ = \int\limits_{}^{} \frac{2(v + 2) + 1}{v + 2} \, dv }$

$\displaystyle \sf{ = \int\limits_{}^{} \bigg[\frac{2(v + 2) }{v + 2} + \frac{1}{v + 2} \bigg] \, dv }$

$\displaystyle \sf{ = \int\limits_{}^{} \bigg[2 + \frac{1}{v + 2} \bigg] \, dv }$

$\displaystyle \sf{ = \int \: 2 \: dv + \int\limits_{}^{} \frac{1}{v + 2} \, dv }$

$\displaystyle \sf{ =2 \int \: \: dv + \int\limits_{}^{} \frac{1}{v + 2} \, dv }$

$\displaystyle \sf{ =2 v + \log \: |v + 2| + c}$

Where C is integration constant

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