- #1
doktorwho
- 181
- 6
Homework Statement
Suggest an integral that is reduced to a rational function integral when this substitution is used:
##a)## ##t=\sin x##
##b)## ##t=\sqrt[6] {x+5}##
##c## ##\sqrt{1-9x^2}=-1+xt##
Homework Equations
3. The Attempt at a Solution [/B]
I found this to be a very interesting problem and wanted to check my results with you. For the first part i think that
a) ##\int \sin x\cos x \, dx## is a good idea couse when we introduce the given substitution we are left with ##\int t \, dt## which is a rational function, right?
For the second part i have some struggles but i think that
b) ##\int \frac{\sqrt[6] {(x+5)^5}}{6\sqrt[6] {x+5}} \, dx## would reduce to ##\int t \, dt##
As for the part c) that i the second Euler substitution and the integral that is suited for it should be any integral of the form c) ##\int \sqrt {ax^2+bx+1} \, dx##
How does this seem to you? Any comments? Any feedback is appreciated