In the following exercises, find each indefinite integral, using appropriate

hadejada7x 2021-12-13 Answered
In the following exercises, find each indefinite integral, using appropriate substitutions.
dx116x2
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Expert Answer

Vivian Soares
Answered 2021-12-14 Author has 36 answers
Step 1
We need to evaluate the following integral
I=dx116x2...(1)
Step 2
Let x=sinu4dx=cosu4du and substitute these in equation (1). We get,
I=1116(sinu4)2(cosu4du)
=14cosu1sin2udu
=14cosucos2udu   1sin2u=cos2u
=14cosucosudu
=14du
=14u+C
=14sin1(4x)+C   x=sinu4u=sin1(4x)
Hence, the integral is
dx116x2=14sin1(4x)+C

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