The discussion focuses on the indefinite integral of functions with specific arguments, particularly examining the forms of ##\cos(x^2)## and ##e^{\tan(x)}##. The argument for the cosine function is identified as ##x^2##, while for the exponential function, it is ##\tan(x)##. The integrand is expressed as ##f(g(x))##, leading to the integral form ##\int f(g(x)) \, dx##. The conversation also raises questions about integrating both functions simultaneously and the implications for their arguments.
PREREQUISITESStudents and educators in calculus, mathematicians focusing on integration techniques, and anyone seeking to deepen their understanding of function arguments in indefinite integrals.
What if both functions are to be integratedBvU said:Hi,
Both are examples of the kind ##f\left( g(x)\right)\ ##.
The argument for ##f()##, the cosine function ##\cos()##, is ##x^2##, so ##g(x) = x^2##.
Similarly, the argument for exponentiation ## f() = \exp() \ ## is ##g(x) = \tan(x)##.
The integrand in both cases is ##f##, so you integrate ##\int f(g(x)) \, dx ##
If both functions are to be integrated what is the argument to integrate?BvU said:Hi,
Both are examples of the kind ##f\left( g(x)\right)\ ##.
The argument for ##f()##, the cosine function ##\cos()##, is ##x^2##, so ##g(x) = x^2##.
Similarly, the argument for exponentiation ## f() = \exp() \ ## is ##g(x) = \tan(x)##.
The integrand in both cases is ##f##, so you integrate ##\int f(g(x)) \, dx ##
? Can you write the form of the integral that you mean ?Michael Santos said:What if both functions are to be integrated