Fleming Boone
07/22/2023 · Junior High School
Evaluate the integral using integration by parts with the indicated choices of \( u \) and \( d v \). (Use \( C \) for the constant of integration.) \[ \int \cos (7 x) d x ; \quad u=x, \quad d v=\cos (7 x) d x \]
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Step-by-step Solution
Calculate the integral \( \int \cos (7x) dx \).
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
\(\int \cos\left(7x\right) dx\)
- step1: Evaluate the integral:
\(\frac{1}{7}\sin\left(7x\right)\)
- step2: Add the constant of integral C:
\(\frac{1}{7}\sin\left(7x\right) + C, C \in \mathbb{R}\)
The integral of \( \int \cos (7x) dx \) using integration by parts with \( u=x \) and \( dv=\cos (7x) dx \) is \( \frac{1}{7}\sin(7x) + C \), where \( C \) is the constant of integration.
Quick Answer
\( \frac{1}{7}\sin(7x) + C \)
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