Integration of a Function with Its Derivative

Rarely Tested

Integration of a Function with Its Derivative

If:

$$u=f(x)$$

then:

$$\int f'(x)f^n(x)\,dx=\frac{f^{n+1}(x)}{n+1}+C$$

for:

$$n\neq-1$$

Usage

- Used when the derivative of an inner function appears as a factor.

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