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## Homework Statement

Use convolution theorem to solve:

[tex]\mathfrak{L} \left \{t\int_{0}^{t} \sin \tau d\tau \right \}[/tex]

Do not solve the integral.

## Homework Equations

"Convolution Theorem" in textbook is stated as:

[tex]\mathfrak{L}\left \{ f*g \right \}=F(s)G(s)[/tex]

[tex]f*g=\int_{0}^{t} \ f(\tau )g(t-\tau ) d\tau[/tex]

## The Attempt at a Solution

Not quite sure how to approach this one with convolution and not solving the integral.

I need a t-τ instead of a t, but I can't have τ's in my Laplace because they won't go to S-space with any meaning.

Answer in book is :

[tex]\frac{3s^2+1}{s^2(s^2+1)^2}[/tex]

working backwards only leads me to a partial fraction type inverse transform.

Thanks in advance for help!

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