Level:
Project ID:
1003018710
Accepted:
1
Clonable:
0
Easy:
0
Four children evaluated the following integral \( I \) on \( (0;\infty) \). Who made a mistake?
\[ I =\int\left(\frac18\sqrt[8]{x^3}+\frac12\sqrt{x^9}-\frac15\sqrt[5]{x^6} \right)\mathrm{d}x \]
Paul: \( I =\frac1{11}\left(x^3\sqrt[8]x+x\sqrt{x^5}-x\sqrt[5]{x^2}\right)+c\text{, }c\in\mathbb{R} \)
Jane: \( I =\frac1{11}\left(x\sqrt[8]{x^3}+x^5\sqrt x-x^2\sqrt[5] x+c\right)\text{, }c\in\mathbb{R} \)
Ann: \( I =\frac1{11}\left(x\sqrt[8]{x^3}+x^5\sqrt x-x^2\sqrt[5]x\right)+c\text{, }c\in\mathbb{R} \)
Miky: \( I =\frac x{11}\sqrt[8]{x^3}+\frac{x^5}{11}\sqrt x-\frac{x^2}{11}\sqrt[5]x+c\text{, }c\in\mathbb{R} \)