Question

Integration By Parts

Hello,

I'm actually having problems with the algebra on this Calculus question. The problem is;

\[\int\limits_{}^{}e^{7x}*\cos(9x)dx\]
So I get all of the Calculus right (confirmed) and get to;
\[\int\limits_{}^{}(1/7)\cos(9x)e^{7x} + (9/7)\sin(9x)e^{7x} - (81/49)\int\limits_{}^{}e^{7x}\cos(9x)\]
So we have the original equation on both sides and need to add that to both sides. This is where I seem to have problems. I know the answer has a denominator of 130, but I keep getting 81. Any help would be greatly appreciated.

Answer 1

the last is the same "kinda" as the first

Answer 2

A = b-2A ; solve for b

Answer 3

i should finish reading before commentling lol

Answer 4

e^(7x) cos(9x) = I
Rest = X

X - (81/49)I = I

X = I + (81/49)I
X / (81/49) = I + I

X / (81/49) = 2I

X / (81/49) / 2 = I

Answer 5

cos(9x)
+ e^7x sin(9x)/9
- 7 e^7x -cos(9x)/81
+ 49 e^7x ............

{S} e^7x cos(9x)=e^7x sin(9x)/9 +7 e^7x cos(9x)/81 -{S} 49 e^7x cos(9x)/81dx

{S} e^7x cos(9x)=e^7x sin(9x)/9 +7 e^7x cos(9x)/81 -49/81{S} e^7x cos(9x)dx
+49/81{S} e^7x cos(9x)dx +49/81{S} e^7x cos(9x)dx
-------------------------------------------------------------------
130{S} e^7x cos(9x) = e^7x sin(9x)/9 +7 e^7x cos(9x)/81
\130 \130

maybe

Answer 6

But how did that 49/81 turn into 130? It feels like magic!

Answer 7

so if i dealt with my signs correctly, and i never do ....

e^7x (sin(9x/9) + 7 cos(9x)/81)
---------------------------
130

Answer 8

A = b - 49/81 A


add 49/81 A to both sides

Answer 9

if my signs are right lol

Answer 10

Right, so then you've got A + (49/81)A = B

Divide by 49/81 on both sides to eliminate, and you've got A + A = B/(49/81)

Answer 11

Or am I just out to lunch with my algebra here? I did the same A = b - 49/81A up above with X and I.

Answer 12

your algebra is off since you cant divide out of a sum

Answer 13

http://www.wolframalpha.com/input/?i=integrate+e%5E%287x%29+cos%289x%29

i was close

Answer 14

i see what i did; 130/81; then multiply thru by 81/130 to clear the left side

Answer 15

all I did was divide off the 130 :)

Answer 16

But where did 130/81 come from?

Answer 17

49 turned into 130 by adding 81 to it? Where'd the 81 come to add to it?

Answer 18

from the mess that you get at the end

1A = stuff - 49/81 A ; ADD 49/81 A to both sides

1A + 49/81 A = stuff

factor out the A

A(1+ 49/81) = stuff

since 1 + 49/81 = 130/81, multiply thru by 81/130

A = 81/130 * stuff

Answer 19

the 81 is the denominator of the constant at the end of all that mess

Answer 20

49/81 is the pulled out constant from your integrations

Answer 21

Oh man.. such a silly freaking mistake.

Answer 22

{S} e^7x cos(9x) dx = e^7x sin(9x)/9 - {S} 7 e^7x sin(9x)/9 dx

...

whew!! glad you see it lol

Answer 23

All from missing the factoring. Amazing how it can just destroy your answer.

Answer 24

yeah, its fun on a test :)

Answer 25

Haha, thats great man. Thanks so much for the help! You've helped me a ton on here :) I hope you're becoming a math professor!! Off to work more homework!

Answer 26

good luck :)