( int x sqrt{x-6} d x )

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Step:1 ：(u = x - 6, d u = d x)Step:2 ：(int (u + 6) sqrt{u} d u)Step:3 ：(int (u^{frac{3}{2}} + 6u^{frac{1}{2}}) d u)Step:4 ：(frac{2}{5}u^{frac{5}{2}} + frac{12}{3}u^{frac{3}{2}} + C)Step:5 ：(frac{2}{5}(x - 6)^{frac{5}{2}} + 4(x - 6)^{frac{3}{2}} + C)

Answer

Step: 1 ：(u = x - 6, d u = d x)Step: 2 ：(int (u + 6) sqrt{u} d u)Step: 3 ：(int (u^{frac{3}{2}} + 6u^{frac{1}{2}}) d u)Step: 4 ：(frac{2}{5}u^{frac{5}{2}} + frac{12}{3}u^{frac{3}{2}} + C)Step: 5 ：(frac{2}{5}(x - 6)^{frac{5}{2}} + 4(x - 6)^{frac{3}{2}} + C)

\( \int x \sqrt{x-6} d x \)

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