f)
[tex]f(x) = 11x \cdot \sqrt[4]{x^3} = 11x \cdot x^{ \frac{3}{4} } = 11x^{\frac{7}{4}} \\ \int\ {11x^{\frac{7}{4}}} \, dx = 11 \int\ {x^{\frac{7}{4}}} \, dx = 11 \cdot \frac{ x^\frac{11}{4} }{\frac{11}{4}} + C= 4x^\frac{11}{4} +C = 4 \sqrt[4]{x^{11}} + C \\= 4x^2\sqrt[4]{x^{3}} + C[/tex]
g)
[tex]f(x) = \frac{1}{ \sqrt[3]{x^2} } = \frac{1}{x^ \frac{2}{3} } = x^{-\frac{2}{3}}\\ \int\ x^{-\frac{2}{3}} \, dx = \frac{x^ \frac{1}{3} }{ \frac{1}{3} } + C= 3x^ \frac{1}{3} + C = 3 \sqrt[3]{x} + C[/tex]
j)
[tex]f(x) = \frac{1}{x-1} \\
\int { \frac{1}{x-1}} \, dx = ln|x-1| + C = ln(x-1) + C[/tex]
Am renuntat la modul deoarece x>1, iar ce este sub modul va fi intotdeauna pozitiv, deci nu mai este nevoie sa pui modul.
