\frac{1}{3!}~ t^2~e^{2t} \

\frac{1}{3}~ t^2~e^{-2t} \

\frac{1}{3!}~ t^2~e^{-3t} \

\frac{1}{6}~ t^3~e^{-2t}

\frac{1+e^{t}}{t}

\frac{1-e^{t}}{t}

\frac{1-e^{-t}}{t}

\frac{1+e^{-t}}{t}

3

0

2

\frac{\pi^7}{ \sqrt[]{7} }

\frac{\pi^3}{ \sqrt[]{14} }

\frac{\pi^6}{ \sqrt[]{7} }

\frac{\pi^3}{ \sqrt[]{7} }

\frac{1+cos 2x}{2 }

\frac{1+cos x}{2 }

\frac{1-cos 2x}{2 }

sine terms only

both cosine and sine terms                        

constant and cosine terms only

4

0

2

2\cos(2t) + 3 \sin(2t)

2\cos(2t) + \frac{3}{2} \sin(2t)

2\cos(4t) + \frac{3}{2} \sin(4t)

2\cos(4t) + 3\sin(4t)

\frac{1}{5}

\frac{1}{3}

\frac{1}{2}

\frac{2~}{s^3}

\frac{2~e^{s}}{s^3}

\frac{2~e^{-s}}{s^3}

\frac{~e^{-s}}{s^2}