integration by parts

Question

ashley1nonly · Answer

x sin(x/7) dx
u=x      du = 1 dx
dv= sin(x/7)dx   v= -7cos(x/7)


x sin(x/7)dx=  -x7cos(x/7)+ /7cos(x/7) dx

u=7   du=0
dv= cos(x/7)  v

ashley1nonly · Answer

my v= 7sin(x/7)

ashley1nonly · Answer

is it right??

misty1212 · Answer

looks good just written weird

ashley1nonly · Answer

sorry didnt know how to get the anti-derivative sign

ashley1nonly · Answer

would the final be

-x 7cos(x/7) + 7 sin(x/7) +c

dumbcow · Answer

yes it looks good

misty1212 · Answer

$$-7x\cos(\frac{x}{7})+7\int \cos(\frac{x}{7})dx$$ i think

misty1212 · Answer

i just meant weird placement of the constants

ashley1nonly · Answer

i took the anti-derivative of cos(x/7)dx

ashley1nonly · Answer

yeah my teacher says that all the time

ashley1nonly · Answer

would you take the anti-derivitive of the last one

misty1212 · Answer

yes

xapproachesinfinity · Answer

yes you need to

misty1212 · Answer

should be easy enough since you sorta did it at the first step

ashley1nonly · Answer

yeah, was my final answer right

misty1212 · Answer

no

misty1212 · Answer

you are off by another 7

misty1212 · Answer

you have 
$$7\int \cos(\frac{x}{7})dx$$ when you take the anti derivative you need another mental u - sub 
multiply by 7 again in other words

ashley1nonly · Answer

7sin(x/7)

misty1212 · Answer

$$\color{red}{49}\sin(\frac{x}{7})$$

ashley1nonly · Answer

-7xcos(x/7)+49sin(x/7)+c

ashley1nonly · Answer

its from multiplying the u time v

misty1212 · Answer

yeah that looks right now

ashley1nonly · Answer

should it be plus the 49 or minus 49

dumbcow · Answer

fyi when its a constant you dont need to use int by parts ... even though it still will give right answer

ashley1nonly · Answer

plus

misty1212 · Answer

the second part is not parts, it is a u sub, but a mental one

ashley1nonly · Answer

thanks so much, hope you guys are here all semester

misty1212 · Answer

$$\color{magenta}\heartsuit$$