Integrals of Exponential Functions
Integrals of exponential functions play a pivotal role in calculus, particularly in areas like differential equations, probability theory, and physics. These integrals involve expressions of the form \( \int e^{ax} \, dx \) or \( \int e^{f(x)} \, dx \), where \( a \) is a constant and \( f(x) \) is a function. Understanding their properties and techniques for their evaluation is fundamental in solving a wide range of mathematical problems. From modeling growth and decay processes to analyzing complex systems, mastering the integration of exponential functions provides a powerful toolset for tackling diverse mathematical challenges.
Questions
- How do you integrate #int ln(e^(2x-1))dx#?
- How do you integrate #f(t) = 1.4e^(0.07t)#?
- How do you integrate #int 5^x-3^xdx# from #[0,1]#?
- How do you integrate #int e^(2x)/(1+e^(2x))dx#?
- How do you integrate #int e^(sinpix)cospix# from #[0,pi/2]#?
- What is #int_0^pi (lnx)^2 / x^(1/2)#?
- How do you find the antiderivative of #((2x)e^(3x))#?
- How do you find the antiderivative of # {(e^x)/ [(e^(2x)) - 1]}#?
- What is the antiderivative of #e^(2x)#?
- How do you integrate #int e^xsqrt(1-e^x)dx#?
- How do you integrate #int x(5^(-x^2))dx#?
- What is the antiderivative of #-ln|cscx+cotx|#?
- How do you integrate #(t^2)e^(4t)#?
- How do you find the integral of #log_8 (2x+1) dx#?
- How do you integrate #int 4^(x/2)dx# from #[-2,2]#?
- What is the integral of #ln(3x)#?
- What is the integral of #ln(sqrt(x))#?
- How do you evaluate the integral #inte^(-x) dx#?
- How do you integrate # (x-1) e^(-x^2+2x) dx#?
- What is the integral of #2e^(2x)#?