Question

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Answer 1

Respuesta:

$\frac{1}{5} *[\frac{4}{7}* x^{\frac{7}{2}} } - \frac{12}{5}* x^{\frac{5}{2}} } + \frac{22}{3}* x^{\frac{3}{2}} }] + C$

Explicación paso a paso:

$\int\limits \frac{(2*x^{3} - 6*x^{2} +11*x)}{5*\sqrt{x} } dx$

$\int\limits\frac{ 2*x^{3}}{5*\sqrt{x} } dx - \int\limits \frac{6*x^{2}}{5*\sqrt{x} } dx + \int\limits \frac{\\11*x}{5*\sqrt{x} } dx$

$\frac{2}{5}* \int\limits\frac{ x^{3}}{\sqrt{x} } dx - \frac{6}{5}* \int\limits \frac{x^{2}}{\sqrt{x} } dx + \frac{11}{5}* \int\limits \frac{\\x}{\sqrt{x} } dx$

$\frac{2}{5}* \int\limits\ x^{3-\frac{1}{2} } } dx - \frac{6}{5}* \int\limits\ x^{2-\frac{1}{2} } } dx + \frac{11}{5}* \int\limits\ x^{1-\frac{1}{2} } } dx$

$\frac{2}{5}* \int\limits\ x^{\frac{5}{2} } } dx - \frac{6}{5}* \int\limits\ x^{\frac{3}{2} } } dx + \frac{11}{5}* \int\limits\ x^{\frac{1}{2} } } dx$

$\frac{\frac{2}{5}}{\frac{5}{2} +1}* x^{\frac{5}{2} +1} } - \frac{\frac{6}{5}}{\frac{3}{2} +1}* x^{\frac{3}{2} +1} } + \frac{\frac{11}{5}}{\frac{1}{2} +1}* x^{\frac{1}{2} +1} } + C$

$\frac{\frac{2}{5}}{\frac{7}{2}}* x^{\frac{7}{2}} } - \frac{\frac{6}{5}}{\frac{5}{2}}* x^{\frac{5}{2}} } + \frac{\frac{11}{5}}{\frac{3}{2}}* x^{\frac{3}{2}} } + C$

$\frac{4}{35}* x^{\frac{7}{2}} } - \frac{12}{25}* x^{\frac{5}{2}} } + \frac{22}{15}* x^{\frac{3}{2}} } + C$

$\frac{1}{5} *[\frac{4}{7}* x^{\frac{7}{2}} } - \frac{12}{5}* x^{\frac{5}{2}} } + \frac{22}{3}* x^{\frac{3}{2}} }] + C$