Question

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Answer 1

Respuesta:

$\int \frac{2x^3-3x+11}{\sqrt{x^5}}=\frac{4}{3}x^{\frac{3}{2}}+\frac{6}{\sqrt{x}}-\frac{22}{3x^{\frac{3}{2}}}+C$

Explicación paso a paso:

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

propiedad de los exponentes.

$\frac{a^n}{a^m}=a^{n-m}\\\\a^{-n}=\frac{1}{a^n}$

$=\int2x^{\frac{1}{2}}-\frac{3}{x^{\frac{3}{2}}}+\frac{11}{x^{\frac{5}{2}}}dx\\\\\int2x^{\frac{1}{2}}dx-\int\frac{3}{x^{\frac{3}{2}}}dx+\int\frac{11}{x^{\frac{5}{2}}}dx$

$\int 2x^{\frac{1}{2}}dx=\frac{4}{3}x^{\frac{3}{2}}$

$\int \frac{3}{x^{\frac{3}{2}}}dx=-\frac{6}{\sqrt{x}}$

$\int \frac{11}{x^{\frac{5}{2}}}dx=-\frac{22}{3x^{\frac{3}{2}}}$

$\int \frac{2x^3-3x+11}{\sqrt{x^5}}=\frac{4}{3}x^{\frac{3}{2}}+\frac{6}{\sqrt{x}}-\frac{22}{3x^{\frac{3}{2}}}+C$