# Obtain the Laplace Transform of Lleft{e^{-2x}+4e^{-3x}right}

Question
Laplace transform
Obtain the Laplace Transform of
$$L\left\{e^{-2x}+4e^{-3x}\right\}$$

2020-12-28
$$\text{step 1}$$
$$\text{laplace transform of }L\left\{e^{-2x}+4e^{-3x}\right\}$$
$$=\int_0^\infty e^{-sx}f(x)dx$$
$$=\int_0^\infty e^{-sx}(e^{-2x}+4e^{-3x})dx$$
$$\text{Step 2}$$
$$=\int_0^\infty (e^{-(s+2)x}+4e^{-(s+3)x})dx$$
$$=\left[\frac{e^{-(s+2)x}}{-(s+2)}+\frac{4e^{-(s+3)x}}{-(s+3)}\right]_0^\infty$$

### Relevant Questions

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