Cook Gardner
09/19/2024 · High School
A intignal Indefinida (a) \( \int\left(5 x^{3}+2 \cos x\right) d x \)
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Calculate the integral \( \int\left(5 x^{3}+2 \cos x\right) d x \).
Evaluate the integral by following steps:
- step0: Evaluate:
\(\int 5x^{3}+2\cos\left(x\right) dx\)
- step1: Use properties of integrals:
\(\int 5x^{3} dx+\int 2\cos\left(x\right) dx\)
- step2: Evaluate the integral:
\(\frac{5}{4}x^{4}+2\sin\left(x\right)\)
- step3: Add the constant of integral C:
\(\frac{5}{4}x^{4}+2\sin\left(x\right) + C, C \in \mathbb{R}\)
A integral indefinida de \( \int\left(5 x^{3}+2 \cos x\right) d x \) é igual a \( \frac{5}{4}x^{4}+2\sin(x) + C \), onde \( C \) é uma constante real.
Quick Answer
A integral indefinida de \( \int\left(5 x^{3}+2 \cos x\right) d x \) é \( \frac{5}{4}x^{4}+2\sin(x) + C \).
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