How To Integrate 1/sqrt(x) + x^(1/3)

Published On :2021-01-28 14:15:00

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[begin{array}{l} smallint frac{{{rm{d}}x}}{{sqrt x + sqrt[{bf{3}}]{x}}}\\ By;Substitution\ ;;;;;;Suppose Rightarrow {z^6} = x;;;;;;;;;;;;;;;;;;;;;;;,;note ldots LCDleft[ {2,3} right] = 6\ 6{z^5}dz = dx\ smallint frac{{6;{z^5}}}{{{z^3} + {z^2}}}dz\ 6smallint frac{{;{z^3}}}{{{z^;} + 1}}dz end{array}]
[begin{array}{l} 6smallint {z^2} - z + 1 - frac{{;1}}{{{z^;} + 1}}dz\ Rightarrow 6left( {;frac{{{z^3}}}{3} - frac{{{z^2}}}{2} + z - ln left| {z + 1} right|;;} right) + c\ Rightarrow 6left( {;frac{{sqrt x }}{3} - frac{{sqrt[3]{x}}}{2} + sqrt[6]{x} - ln left| {sqrt[6]{x} + 1} right|;;} right) + c end{array}]