Valdez Burns
01/28/2024 · Junior High School
1. Evaluar \[ \int\left(\frac{5}{\sqrt{s^{2}}}+\frac{2}{\sqrt{s^{3}}}\right) d s \] a) conteste correctamentel
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Calculate or simplify the expression \( \int\left(\frac{5}{\sqrt{s^{2}}}+\frac{2}{\sqrt{s^{3}}}\right) d s \).
Evaluate the integral by following steps:
- step0: Evaluate:
\(\int \frac{5}{\sqrt{s^{2}}}+\frac{2}{\sqrt{s^{3}}} ds\)
- step1: Evaluate the power:
\(\int \frac{5}{s}+\frac{2}{\sqrt{s^{3}}} ds\)
- step2: Evaluate the power:
\(\int \frac{5}{s}+\frac{2}{s^{\frac{3}{2}}} ds\)
- step3: Use properties of integrals:
\(\int \frac{5}{s} ds+\int \frac{2}{s^{\frac{3}{2}}} ds\)
- step4: Evaluate the integral:
\(5\ln{\left(s\right)}-\frac{4}{s^{\frac{1}{2}}}\)
- step5: Simplify:
\(5\ln{\left(s\right)}-\frac{4\sqrt{s}}{s}\)
- step6: Add the constant of integral C:
\(5\ln{\left(s\right)}-\frac{4\sqrt{s}}{s} + C, C \in \mathbb{R}\)
La integral de la expresión dada es \(5\ln(s) - \frac{4\sqrt{s}}{s} + C\), donde \(C\) es una constante real.
Quick Answer
La integral es \(5\ln(s) - \frac{4\sqrt{s}}{s} + C\).
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