Mathematics

Integrate:
$$\int \dfrac{x+2^x.\log 2}{x^2+2^{x+1}}dx$$


SOLUTION
$$I=\displaystyle\int\dfrac{x+2^{x}.\log 2}{x^{2}+2^{x+1}}dx$$

Let $$u=x^{2}+2^{x+1}$$

$$\Rightarrow du=2x+2^{x+1}\log 2dx$$
$$=2(x+2^{x}\log 2)dx$$

Substituting

$$I=\displaystyle\int\dfrac{du}{2u}$$$

$$=\dfrac{1}{2}\log u+C$$

$$I=\dfrac{1}{2}\log (x^{2}+2^{x+1})+C$$
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Subjective Medium Published on 17th 09, 2020
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