Reduction Formula for Exponential-Power Integral

Rarely Tested

Reduction Formula for Exponential-Power Integral

Define:

$$I_n=\int x^ne^{ax}\,dx$$

Then:

$$I_n=\frac{x^ne^{ax}}{a}-\frac{n}{a}I_{n-1}$$

Usage

- Used to reduce integrals involving powers of $$x$$ multiplied by an exponential function.

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