Evaluate the integrals in Exercises 51–56. 51. sin 3x cos 2x dx 52. sin 2x cos 3x dx sin x cos x dx 53. sin 3x sin 3x dx 54. /2 55. cos 3x cos 4x dx 56. cos x cos 7x dx T/2

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A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

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A: Topic = Integration

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A:

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A: Given: verify that ∫cotxdx=lnsinx+c For verifying given integral, we integrate given integral

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A: Use the integration by parts to simplify.

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Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

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A: 47. ∫sech2x-12 dx48. ∫ csch25-x dx

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Q: Evaluate the integrals in Exercises :: 1. / sinh 2x dx sinh đx 41. 42.

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A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

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A: We know that ∫abxmdx=xm+1m+1ba=1m+1(bm+1-am+1) ; m≠-1 We will solve the given integral using this…

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Q: Evaluate the integrals: (g)∫sin2xcos3x dx. (h)∫sin5x dx. (i)∫sin(ln(3x)) / 2x dx.

A: We have to evaluate given integrals. ∫sin2xcos3x dx.   ∫sin5x dx. ∫sin(ln(3x)) / 2x dx.

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A: NOTE: Refresh your page if you can't see any equations. . use integration by parts the rule is

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A: To find the integral: ∫sinxcos2x-3cosxdx Let substitute t=cosx Differentiating both sides,…