# SOLVED: Evaluate the following integral using integration by parts. âˆ« (x cos x) dx Use the integration by parts formula so that the new integral is simpler than the original one. Choose: A. âˆ« (x s

Calculus 2: How Do You Integrate? (11 of 300) Find the Integral of … 1/x (Method 2)
Calculus 2: How Do You Integrate? (11 of 300) Find the Integral of … 1/x (Method 2)

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Evaluate the following integral using integration by parts.
âˆ« (x cos x) dx
Use the integration by parts formula so that the new integral is simpler than the original one. Choose:
A. âˆ« (x sin x) dx
B. âˆ« (sin x) dx
C. âˆ« (cos x) dx
D. âˆ« (cos x) dx
Evaluate the integral:
âˆ« (x cos x) dx =
(Type an exact answer; Use as needed)

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a. âˆ«x sin(x)dx = x(-cos(x)) – âˆ«(-sin(x))dxb. âˆ«x sin(x)dx = -x cos(x) – âˆ«sin(x)dxc. âˆ«x sin(x)dx = -x cos(x) + âˆ«cos(x)dxd. âˆ«x sin(x)dx = x sin(x) – âˆ«(-sin(x))dx

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Evaluate $\displaystyle \int \sin x \cos x dx$ by four methods:

(a) the substitution $u = \cos x$ (b) the substitution $u = \sin x$ (c) the identity $\sin 2x = 2 \sin x \cos x$ (d) integration by partsExplain the different appearances of the answers.

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