What Is The Integral Of Ln X A slightly different method The integral is I ln 2x 2dx 2 ln2xdx Perforn an integration by parts uv dx uv u vdx u ln2x u 1 2 x 2 1 x v 1 v x
See below We must use integration by parts for this problem We let u ln x 1 and dv x It follows that int u dv uv int vdu int ln x 1 x dx 1 2x 2ln x 1 int 1 2x 2 1 1 make sure that the degree of your denominator is greater than the degree of your numerator 2 factorize the denominator 3 perform the partial fraction decomposition 4
What Is The Integral Of Ln X
What Is The Integral Of Ln X
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How do I find the integral of f x sec5 x Calculus Techniques of Integration Integration by Trigonometric Substitution How do you evaluate the integral x4 x2 1 dx
I int ln 3x 4 dx 3x 4 ln 3x 4 1 3 C We seek I int ln 3x 4 dx First we perform a substitution Let t 3x 4 dt dx 3 Substituting into the integral we get I Int x a 3 x 3 dx 1 6a ln x 2 ax a 2 sqrt 3 3a arctan 2x a sqrt 3 a 1 3a ln x a C We seek I int x a 3 x 3 dx We can factorize the integrand
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The answer is ln4 Recall that the FTC is a powerful statement it allows us to compute area under the curve just by finding antiderivatives So the best thing that you can do One way to do this is to pick values for x which will cancel each variable x 2 1 B 4 1 1 5B B 1 5 x 1 2 1 A 1 2 2 1 A 5 2 A 2 5 We put these values
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A slightly different method The integral is I ln 2x 2dx 2 ln2xdx Perforn an integration by parts uv dx uv u vdx u ln2x u 1 2 x 2 1 x v 1 v x
https://socratic.org › questions
See below We must use integration by parts for this problem We let u ln x 1 and dv x It follows that int u dv uv int vdu int ln x 1 x dx 1 2x 2ln x 1 int 1 2x 2 1
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