find all antiderivatives for the following function. f(x)=7 sec²x the antiderivatives of f(x)=7 sec²x are…

Explanation:

Step1: Recall antiderivative rule

The antiderivative of $\sec^{2}x$ is $\tan x$.

Step2: Apply constant - multiple rule

If $F(x)$ is an antiderivative of $f(x)$ and $k$ is a constant, then the antiderivative of $kf(x)$ is $kF(x)$. Here $k = 7$ and $f(x)=\sec^{2}x$. So the antiderivative of $7\sec^{2}x$ is $7\tan x + C$, where $C$ is an arbitrary constant.

Answer:

$7\tan x + C$