Calculus

Antiderivatives

Integration of Logarithmic Functions

         

If xf(x)=24lnx,xf'(x)=24\ln x, what is the function f(x)?f(x)? (Use CC as the constant of integration.)

If f(x)f(x) is a function such that f(x)=1xlnx+3dxf(x)=\int \frac{1}{x \sqrt{\ln x+3}} dx and f(e)=21,f(e)=21, what is the value of f(e5)?f(e^{5})?

What is the indefinite integral1x(7(lnx)6+5)dx?\int \frac{1}{x}\left(7(\ln x)^{6}+5\right) dx? (Use CC as the constant of integration.)

Let N=1e8ln(1x)dxN = \displaystyle \int_{1}^{e^ 8} \ln \left( \dfrac {1}{x} \right) \, dx. If N=aebcN = -ae^b - c, where aa, bb and cc are positive integers and ee is the base of the natural logarithm, what is the value of a+b+ca + b + c?

If f(x)f(x) is a function satisfying f(x)=6(lnx)5xdxf(x)=\int \frac{6(\ln x)^{5}}{x} dx and f(e)=8, f(e)=8, what is the value of f(e2)?f(e^2)?

×

Problem Loading...

Note Loading...

Set Loading...