Evaluate the following integrals. Include absolute values only when needed.

Josalynn 2021-10-15 Answered
Evaluate the following integrals. Include absolute values only when needed.
sin(lnx)4xdx
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Expert Answer

Talisha
Answered 2021-10-16 Author has 93 answers
It is given that, sin(ln(x))4xdx
We have to evaluate it.
We have, sin(ln(x))4xdx
Let u=ln(x)
differentiate equation w.r.t x we get
du=1xdx,dx=xdu
Then equation becomes
sin(ln(x))4xdx=14sin(u)du
sin(ln(x))4xdx=14(cos(u))+C, where C is arbitrary constant
Putting the value of u=ln(x) in above equation, we get
sin(ln(x))4xdx=14(cos(u))+C
Hence, sin(ln(x))4xdx=cos(ln(x))4+C
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