The discussion revolves around the integration of a function involving a negative exponent, specifically the integral of \(\frac{-2x}{\sqrt[4]{x+2}}\). Participants are exploring the validity of substitution in this context.
Some participants affirm the substitution approach, while others raise concerns about the treatment of the exponent in the context of the original problem. There is acknowledgment of a mistake regarding the exponent's sign, indicating a productive direction in the discussion.
Participants are working under the constraints of proper substitution rules and the implications of negative exponents in integration. The original problem's setup is also being scrutinized for accuracy.
theRukus said:Homework Statement
[itex]\int \frac{-2x}{\sqrt[4]{x+2}}dx[/itex]
The Attempt at a Solution
[itex]=-2*\int x(x+2)^{1/4}dx[/itex]
Let [itex]u=x+2[/itex].
Then, [itex]u-2=x[/itex],
and [itex]du = dx[/itex]
.. Continued from above,
[itex]=-2*\int (u-2)u^{1/4}du[/itex]
[itex]=-2*\int u^{5/4}-2u^{1/4}du[/itex]
Is that last step allowed?
SteamKing said:Except the exponent (1/4) must be negative since the factor (x+2)^(1/4) was in the denominator in the OP.