`\int` $\frac{1}{\sqrt[5]{x}}$ dx= `\int` $\frac{1}{\sqrt[9]{x³}}$ dx= `\int` $\frac{1}{\sqrt[2]{x}}$ dx= `\int` $\frac{x^{2}-x+1}{\sqrt[]{x}}$ dx=...

Đáp án:

Giải thích các bước giải:

 `\int\ \frac{1}{\root[5]{x}} dx`

`=\int\ \frac{1}{x^{1/5}} dx`

`=\int\ x^{-1/5} dx`

`=5/4 x^{4/5}+C`

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 `\int\ \frac{1}{\root[9]{3}} dx`

`=\int\ \frac{1}{x^{1/3}} dx`

`=\int\ x^{-1/3} dx`

`=3/2 x^{2/3}+C`

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 `\int\ \frac{1}{\root[2]{x}} dx`

`=\int\ \frac{1}{x^{1/2}} dx`

`=\int\ x^{-1/2} dx`

`=2 x^{1/2}+C`

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 `\int\ \frac{x^2-x+1}{\sqrt{x}} dx`

 `=\int\ \frac{x^2}{\sqrt{x}} dx-\int\ \frac{x}{\sqrt{x}} dx+\int\ \frac{1}{\sqrt{x}} dx`

 `=\int\ x^{3/2} dx-\int\ x^{1/2} dx+\int\ x^{-1/2} dx`

`=2/5 x^{5/2} + 2/3 x^{3/2}+2x^{1/2}+C`