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LN(x) DX. set. U = LN(x), DV = DX. then we find. Du = (1/x) DX, v = x. substitute. Ln(x) DX = u DV. and use integration by parts. = UV — v Du. substitute u=LN(x), v=x, and Du=(1/x)DX.
LN(x) DX = x LN(x) — x + C.
8:30 19:20 Suggested clip Integration of Logarithmic Functions By Substitution & Using Long YouTubeStart of suggested client of suggested clip Integration of Logarithmic Functions By Substitution & Using Long
The derivative of the logarithmic function is given by: f (x) = 1 / (x LN(b)) x is the function argument. B is the logarithm base. Ln b is the natural logarithm of b.
Antiderivative and the Indefinite Integral (F(x)+C)=F(x)+C=f(x)+0=f(x). In this definition, the is called the integral symbol, f(x) is called the integral, x is called the variable of integration, DX is called the differential of the variable x, and C is called the constant of integration.
Declare a variable u and substitute it into the integral: Differentiate u = 4x + 1 and isolate the x term. This gives you the differential, Du = 4dx. Substitute Du/4 for DX in the integral: Evaluate the integral: Substitute back 4x + 1 for u:
6:15 12:55 Suggested clip How to Integrate Quickly ~ 11 Speedy Integrals Using the 'Chain YouTubeStart of suggested client of suggested clip How to Integrate Quickly ~ 11 Speedy Integrals Using the 'Chain
Choose u and v. Differentiate u: u' Integrate v: v DX. Put u, u' and v DX into: UV DX u' (v DX) DX. Simplify and solve.

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