Question

Evaluate the integral. $\int\left(x^2+2 x\right) \cos x d x$

   Evaluate the integral.
$\int\left(x^2+2 x\right) \cos x d x$

Calculus

James Stewart 7th Edition

Chapter 7, Problem 7

Instant Answer

Solved by Expert Robert Daugherty

05/14/2020

Step 1

The formula is: $\int u(x)v'(x) \, dx = u(x)v(x) - \int v(x)u'(x) \, dx$ Show more…

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Evaluate the integral. $\int\left(x^2+2 x\right) \cos x d x$

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Key Concepts

Integration by Parts

Integration by parts is a technique derived from the product rule of differentiation. It is particularly useful when integrating the product of two functions by selecting one part to differentiate (u) and another to integrate (dv), which simplifies the integration process.

Trigonometric Integration

Trigonometric integration involves methods for integrating functions that include trigonometric terms such as cosine. Understanding the antiderivatives of trigonometric functions, like the fact that the antiderivative of cos(x) is sin(x), is essential in applying techniques such as integration by parts.

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