# Math Help - integration problems

1. ## integration problems

25.) integrate
xsqrt(x-5) dx

i think this is integration by parts with u = x and dv = x-5 is this correct?

35.) integrate
e^(2x) * sinx dx

u = sinx dv = e^(2x)

i end up doing integration by parts 1 time and then i find i have to do it again

after the 2nd integration of parts i end up with.......
(sinx)(e^(2x))-(cosx)(e^(2x)) + integral of | e^(2x)(sinx)

the problem is the bolded part is the original equation...but when i move it to the other side it cancels out the problem...i have no idea what i am doing wrong -thx

2. For the first problem, integration by parts is not needed. Just let u = x-5.

For the second problem, you made a sign error somewhere.

3. $\int e^{2x} \sin x \ dx = -e^{2x} \cos x + 2e^{2x} \sin x - 4 \int e^{2x} \sin x \ dx$

4. ## k

ok i got the second one....but the first one i still dont understand

how can u let u = x-5...it wont make the x in the front of the problem disappear ??

5. Originally Posted by maybnxtseasn
[snip]
but the first one i still dont understand

how can u let u = x-5...it wont make the x in the front of the problem disappear ??
Have you not been taught the technique of u-substitution?

6. Originally Posted by maybnxtseasn
ok i got the second one....but the first one i still dont understand

how can u let u = x-5...it wont make the x in the front of the problem disappear ??
If $\displaystyle u = x - 5$ then $\displaystyle x = u + 5$...