Question

Integration by parts what is this final answer i can't seem to get it

Answer 1

\[\int\limits_{0}^{\Pi/2} \cos(x) e^x dx\]

Answer 2

not sure exactly what the final answer is i got aprox 2.47026

Answer 3

@Kainui

Answer 4

wolfram says `1.9`
http://www.wolframalpha.com/input/?i=%5Cint%5Climits_%7B0%7D%5E%7B%5CPi%2F2%7D+%5Ccos%28x%29+e%5Ex+dx

Answer 5

thank you can u help me with integration by parts \[\int\limits x(x+1)^5 dx\]

what is the u = ? dv=? du=? v=?

Answer 6

@ganeshie8

Answer 7

Let u = x+1 du = dx

Answer 8

you will need to have the parenthetical statement as a substitution.

Answer 9

No need for parts

Answer 10

my online assignment is asking for u,du,dv,v though

Answer 11

Well what I usually like to do is let dv = the most complicated thing you can integrate

Answer 12

So u = ? dv = ? :P

Answer 13

so is it u= x du= 1 dv= (x+1)^5 and v = (x+1)^6 ?

@astrophysics

Answer 14

u = x
du = dx
dv = (x+1)^5 dx
v = 1/6(x+1)^6

Answer 15

1/6(x+1)^6-1/42(x+1)^7+c final answer?

Answer 16

@Astrophysics

Answer 17

\[\frac{ x^7 }{ 7 }+\frac{ 5x^6 }{ 6 }+2x^5+\frac{ 5x^4 }{ 2 }+\frac{ 5x^3 }{ 3 }+\frac{ x^2 }{ 2 }+C\]

http://www.wolframalpha.com/input/?i=integrate+x%28x%2B1%29%5E5

Answer 18

You're sort of close,

u = x+1, du = dx

\[\int\limits (u-1)u^5du \implies \int\limits (u^6-u^5)du\]

etc, etc,
\[\frac{ 1 }{ 42 }(x+1)^6(6x+1)+C\]

Answer 19

thank you i got it

Answer 20

Good job :)