Evaluate the following definite integrals. int_{1/8}^1frac{dx}{xsqrt{1+x^{2/3}}}

Jaya Legge 2020-12-14 Answered
Evaluate the following definite integrals.
1/81dxx1+x2/3
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Expert Answer

wornoutwomanC
Answered 2020-12-15 Author has 81 answers

Consider the integral:1/81dxx1+x2/3
Apply u-substitution: u=1+x2/3
1/81dxx1+x2/3=51/2223u21du
=351/2221u21du
=351/2221(u2+1)du
=351/2221u2+1du
=3([ln|u+1|2ln|u1|2]51/222)
=3[12(ln|u+1|ln|u1|)]51/222
=3ln(2+1)ln(21)ln(52+1)+ln(521)2Answer in terms of logarithms:
1/81dxx1+x2/3=3ln(2+1)ln(21)ln(52+1)+ln(521)2

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