Let f(x)=\cos (\ln x) (a) Find the absolute extreme… SolvedLib

Integral of cos(ln(x)) (by parts) YouTube

The integral of cos (lnx) is an antiderivative of cos (ln x) function which is equal to ½ [xsin (ln x) + xcos (ln x)]. It is also known as the reverse derivative of sine function which is a trigonometric identity. The sine function is the ratio of adjacent side to the hypotenuse of a triangle which is written as: cos = adjacent side / hypotenuse

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Example 3.5.2: Finding the Derivative of a Function Containing cos x. Find the derivative of g(x) = cosx 4x2. Solution. By applying the quotient rule, we have. g′ (x) = ( − sinx)4x2 − 8x(cosx) (4x2)2. Simplifying, we obtain. g′ (x) = − 4x2sinx − 8xcosx 16x4 = − xsinx − 2cosx 4x3.

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We calculate the definite integral of ln(cos x) over the interval from 0 to pi/2.Playlist: https://youtube.com/playlist?list=PL22w63XsKjqzJpcuD6InKWZXep2L0z1.

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so basically the derivative of a function has the same domain as the function itself. Therefore the derivative of the function f (x)= ln (x), which is defined only of x > 0, is also defined only for x > 0 (f' (x) = 1/x where x > 0). i hope this makes sense. ( 2 votes)

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Cos(ln x) dx = 11_(a) sin (In x) + c(b) COS (In x) + … SolvedLib

1 Answer Jim H Aug 30, 2015 Integrate by parts (twice). Explanation: Looking at ∫cos(lnx)dx, we realize that if can't integrate straight away. Next thought is, perhaps we could use substitution. We would need cos(lnx) 1 x to integrate by substitution.

Let f(x)=\cos (\ln x) (a) Find the absolute extreme… SolvedLib

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Figure 6.2.7: Setting up Integration by Parts. Putting this all together in the Integration by Parts formula, things work out very nicely: $$\int \ln x\,dx = x\ln x - \int x\,\frac1x\,dx.\] The new integral simplifies to ∫ 1dx, which is about as simple as things get. Its integral is x + C and our answer is.