annie1799
Answered

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Evaluate x[tex]x^{2} \sqrt{(x^3+9)}[/tex]with subsititution using u=x^3+9

Sagot :

LammettHash

It sounds like you're talking about an integral, namely

[tex]\displaystyle\int x^2\sqrt{x^3+9}\,\mathrm dx[/tex]

Substitute u = x ³ + 9, so that du = 3x ² dx. Then

[tex]\displaystyle\int x^2\sqrt{x^3+9}\,\mathrm dx=\frac13\int\sqrt{u}\,\mathrm du=\frac13\times\frac23u^{\frac32}+C=\boxed{\frac29(x^3+9)^{\frac32}+C}[/tex]

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