anti-derivative of y=2^-x ?

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Answer 1 · 2018-01-21T01:37:55

#(-2^-x)/ln2+C#

To find the antiderivative of #y=2^-x#, we need to integrate it. That means, the antiderivative of #2^-x# is equal to

#int2^-xdx#

We can use u-substitution for this integral.

Let #u=-x#, #du=-1 \ dx#, #dx=-du#

#:.=int2^u*-du#

#int-2^udu#

#-int2^udu#

Know that, #inta^xdx=a^x/(lna)#

#:.=-(2^u)/ln2+C#

Substitute #u=-x# back in, we get

#(-2^-x)/ln2+C#

anti-derivative of y=2^-x ? ​​