Question

How do i integrate this by parts x^11sin(x^6)dx?

Answer 1

\[\int x^{11}Sin(x^6)dx\]

Answer 2

?

Answer 3

U sub

u= x^6

du = 6x^5

Answer 4

du* u= 6 x^11

Answer 5

\[\frac{1}{6}\int u Sin(u) du \]

Answer 6

do integration by parts

a = u db= sin(u)

da= 1 du b= -Cos(u)

Answer 7

-u Cos(u)+ \[\int Cos(u) du\]

\[\frac{1}{6}(-u Cos(u)+ Sin(u)+C)\]

Answer 8

u= x^6

thus put that back in

\[\frac{1}{6}(-x^6 Cos(x^6)+ Sin(x^6)+C)\]

Answer 9

how did you get (1/6)?

Answer 10

du* u= 6 x^11

we want

x^11

so we divide by 6