Solve. displaystyleintfrac{{sqrt{{x}}}}{{{1}+{sqrt[{{3}}]{{x}}}}}{left.{d}{x}right.}=?

sagnuhh 2020-10-25 Answered
Solve. x1+x3dx=?
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Expert Answer

casincal
Answered 2020-10-26 Author has 82 answers
Notice that if u=x16,then u2=x13andu3=x12.
Also we have that du=16x56dx=16u5dx.
So that,
21+x13dx=6u5u31+u2du=6u81+u2
From here, we can simply use some polynomial division to simplify the quotient.Notice then that:
u81+u2=u6u4+u21+1u2+1
Thus, we have the folowing:
6u81+u2du=6(u6u4+u21+1u2+1)du
So we have the last result:
6(u6u4+u21+1u2+1)du=6u776u55+6u336u+6arctanu)
6x7676x565+6x1236x16+6arctanx13
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