Question

Tính nguyên hàm:

\(f\left(x\right)=\sqrt{x\sqrt{x\sqrt{x}}}\)

\(f\left(x\right)=\sqrt{x^4+x^{-4}+2}\)

 

Answer 1

𝕙𝕒𝕖𝕟𝕘𝟚𝟘𝟙𝟘

Answer 2

\(f\left(x\right)=\sqrt{x\sqrt{x\sqrt{x}}}\)

\(\Leftrightarrow f\left(x\right)=\sqrt{x.x^{\dfrac{1}{2}}.x^{\dfrac{1}{4}}}=\sqrt{x^{\dfrac{7}{4}}}=x^{\dfrac{7}{8}}\)

\(\int f\left(x\right)dx=\int x^{\dfrac{7}{8}}dx=\dfrac{x^{\dfrac{7}{8}+1}}{\dfrac{7}{8}+1}+C=\dfrac{8x^{\dfrac{15}{8}}}{15}+C\)