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

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

Question
Laplace transform
asked 2020-12-27
Obtain the Laplace Transform of
\(L\left\{e^{-2x}+4e^{-3x}\right\}\)

Answers (1)

2020-12-28
\(\text{step 1}\)
\(\text{laplace transform of }L\left\{e^{-2x}+4e^{-3x}\right\}\)
\(=\int_0^\infty e^{-sx}f(x)dx\)
\(=\int_0^\infty e^{-sx}(e^{-2x}+4e^{-3x})dx\)
\(\text{Step 2}\)
\(=\int_0^\infty (e^{-(s+2)x}+4e^{-(s+3)x})dx\)
\(=\left[\frac{e^{-(s+2)x}}{-(s+2)}+\frac{4e^{-(s+3)x}}{-(s+3)}\right]_0^\infty\)
0

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