Asked by <3
Evaluate the indefinite integral.
(e^7x)/(e^14x+16)dx
(e^7x)/(e^14x+16)dx
Answers
Answered by
MathMate
Use the substitution:
u=e^(7x)
then
du = 7e^(7x)dx
and the integral
I=∫e^(7x)/(e^(14x)+16)dx
=(1/7)∫du/(u²+16)
which is a standard form that for arctan
=(1/7)(1/4)tan<sup>-1</sup>(u/4)
Back-substitute u=e^(7x) into the expression to get the answer in terms of x.
u=e^(7x)
then
du = 7e^(7x)dx
and the integral
I=∫e^(7x)/(e^(14x)+16)dx
=(1/7)∫du/(u²+16)
which is a standard form that for arctan
=(1/7)(1/4)tan<sup>-1</sup>(u/4)
Back-substitute u=e^(7x) into the expression to get the answer in terms of x.
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