Mathematics

Find proper substitution
$$\int _{ 0 }^{ 1 }{ \dfrac { { e }^{ -x } }{ 1+{ e }^{ -x } } dx }$$


ANSWER

$$1+{ e }^{ -x }\rightarrow t$$


SOLUTION
$$\int _{ 0 }^{ 1 }{ \cfrac { { e }^{ -x } }{ 1+{ e }^{ -x } } dx } $$
$$1+{ e }^{ -x }=t$$
$$\Rightarrow { -e }^{ -x }dx=dt$$
$$\int _{ 0 }^{ 1 }{ \cfrac { -dt }{ t }  } \quad \therefore 1+{ e }^{ -x }=t$$
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Single Correct Medium Published on 17th 09, 2020
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