What's wrong with my answer? (Integration)?

have faith young person...your work is correct...to find a value for " c " demands that additional information has to be given...that is c = 4 is a valid response , as well as c = 54

note : the " answer book " used w = 2 + √x and then forgot to add the ' + C '

like your's better

Hi

You got the same answer. The link you gave doesn't include the constant of integration, which the 4 would be part of. So the answer the link should've gave (at the very least), is:

2*sqrt(x) - 4*log(sqrt(x) + 2) + 4 + C (they mean log as in natural log)

Then since 4 plus an arbitrary constant is another arbitrary constant, we can simplify that to:

2*sqrt(x) - 4*log(sqrt(x) + 2) + C

Which is the answer you got.

I hope this helps!

Your answer matches the one given by that website if you let c = 2.

Some people use log to represent the natural log (instead of base 10). That's why they have log instead of ln. √x + 2 is always positive so the absolute value isn't necessary. You can replace the absolute value with parentheses.

Your answer is correct; you can just simplify it a bit further...

2[√x − 2(ln(2 + √x))] + c

= 2√x − 4ln(2 + √x) + c

Why that site made c = 4 I don't know, but c can be any value in this case.

I = ? cos(2x)e^4x dx = e^4x ? cos2x dx - ? [d/dx(e^4x) ? cos2x dx] dx = (a million/2) e^4x sin2x - 2 ? e^4x sin2x dx = (a million/2) e^4x sin2x - 2 [ e^4x ? sin2x dx - ? [d/dx(e^4x) ? sin2x dx] dx ] = (a million/2) e^4x sin2x + e^4x cos2x - 4? e^4x cos2x dx + 5c = (a million/2) e^4x sin2x + e^4x cos2x - 4 I +5c => 5 I = (a million/2) e^4x sin2x + e^4x cos2x - 4 I +5c => I = (a million/10) e^4x sin2x + (2/10) e^4x cos2x + c => I = [(e^4x)/10] (sin2x + 2cos2x) + c. notice: you additionally can use the formulation ? e^ax cosbx dx = [e^ax / (a^2 + b^2)] * (acosbx + bsinbx) that is derived in my unfastened academic web site of math/physics, hyperlink of that is as under. See corollary of knowledge 14 interior the hyperlink.