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evaluate ∫ (x^(-1/3) + sqrt(x) + 2)/cube root(x) dx

evaluate
∫ (x^(-1/3) + sqrt(x) + 2)/cube root(x) dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{x^{-1/3}+\sqrt{x}+2}{x^{1/3}}dx
I = \int (x^{-2/3}+x^{1/6}+2x^{-1/3})dx
I = \int x^{-2/3}dx+\int x^{1/6}dx+\int 2x^{-1/3}dx
I = 3x^{1/3}dx+\int x^{1/6}dx+\int 2x^{-1/3}dx
I = 3x^{1/3}dx+\frac{6}{7}.x^{7/6}dx+3x^{2/3}+c

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