Davies Norris
10/20/2023 · Senior High School
b) \( \int\left(2 x^{-3}+2 x^{-2}-x^{-1}\right) d x \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate the integral \( \int\left(2 x^{-3}+2 x^{-2}-x^{-1}\right) d x \).
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
\(\int \left(2x^{-3}+2x^{-2}-x^{-1}\right) dx\)
- step1: Evaluate:
\(\int 2x^{-3}+2x^{-2}-x^{-1} dx\)
- step2: Use properties of integrals:
\(\int 2x^{-3} dx+\int 2x^{-2} dx-\int x^{-1} dx\)
- step3: Evaluate the integral:
\(-x^{-2}-2x^{-1}-\ln{\left(\left|x\right|\right)}\)
- step4: Simplify:
\(-\frac{1}{x^{2}}-2x^{-1}-\ln{\left(\left|x\right|\right)}\)
- step5: Simplify:
\(-\frac{1}{x^{2}}-\frac{2}{x}-\ln{\left(\left|x\right|\right)}\)
- step6: Add the constant of integral C:
\(-\frac{1}{x^{2}}-\frac{2}{x}-\ln{\left(\left|x\right|\right)} + C, C \in \mathbb{R}\)
La integral de \( \int\left(2 x^{-3}+2 x^{-2}-x^{-1}\right) d x \) es igual a \( -\frac{1}{x^{2}}-\frac{2}{x}-\ln{(|x|)} + C \), donde \( C \) es una constante real.
Quick Answer
La integral es \( -\frac{1}{x^{2}}-\frac{2}{x}-\ln{(|x|)} + C \).
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