## anonymous 5 years ago int_{}^{?}e ^{4t}sin3t

1. anonymous

integrate $\int\limits_{}^{?}e ^{4t}\sin3t$

2. anonymous

$\int\limits e ^{4t} \sin3t dt ?$

3. anonymous

can be solved by integration by parts

4. anonymous

$e ^{4t} -\cos3t/3 -\int\limits -\cos3t/3.e ^{4t} 4 dt$

5. anonymous

$\cos3t.e ^{4t} /3 +(4/3)\int\limits e ^{4t} \cos 3t d t$

6. anonymous

oh i missed the negative sign -(cos3t.e4t)/3+(4/3)∫e4tcos3tdt

7. anonymous
8. anonymous

yea its by using the formula

9. anonymous

Yeah, you will never finish integrating but you will get a multiple of the original integral eventually...so you move it to the other side of the equation and combine with the original integral and, shazam!, you are done.