The indefinite integral and its "argument"

[Michael Santos]

Homework Statement

The indefinite integral $$\int \, $$ and it's argument.
The indefinite integral has a function of e.g $\cos (x^2) \$ or $\ e^{tan (x)} \$
If the argument of $\cos (x^2) \$ is $\ x^2 \$ then the argument of $\ e^{tan(x)} \$ is $\ x \$ or $\ tan (x) \$ ?

Homework Equations

The Attempt at a Solution

 

[BvU]

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 $\int f(g(x)) \, dx$

 

[Michael Santos]

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 $\int f(g(x)) \, dx$

What if both functions are to be integrated

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]

What if both functions are to be integrated

? Can you write the form of the integral that you mean ?