Question

int (x^2)(cosx)dx please help :)

Answer 1

so where did you stuck

Answer 2

hmmm ok ive got u=cosx
du=-sinx
dv=x^2dx
v=x^3/3

Answer 3

\[x ^{3}cosx-\int\limits_{}^{}-x^3sinxdx\]

Answer 4

well x^3sinxdx/3

Answer 5

eh you are complicating things up
why don't you pick u=x^2 and dv=cosx

Answer 6

ah yeah that is a bit cleaner

Answer 7

we are trying to avoid x^3 and sort of expressions

Answer 8

so v=sinx right

Answer 9

now redo the Integral by part

Answer 10

no! if dv=cosx
v=-sinx

Answer 11

i need to take a second substitution... so im guessing u-2x and dv=sinx?

Answer 12

oh hold on sorry you are right

Answer 13

i always get confused with the sinx and cosx derivatives and which is negative... lol

Answer 14

yes! go for it now

Answer 15

ok so du=xdx and v=-cosx

Answer 16

Don't worry we all do such mistakes just recheck your stuff by differentiating and see if that's true

Answer 17

do i need to do a third sub here?

Answer 18

i end up with x^2sinx+2xcosx-int(-xcosxdx)

Answer 19

v=sinx not cosx i said you are right

Answer 20

wait i meant v=-cosx for the second substitution

Answer 21

so u=x^2 dv=cosx
du=2x v=sinx
just make sure this is what you have ok

Answer 22

for the first sub yes

Answer 23

then with that i get
x^2sinx-intsinx2xdx

Answer 24

oh second int by part you -2"intxsinx"

Answer 25

yeah

Answer 26

ah do i have to pull the 2 out or can i just make u=2x

Answer 27

nah probably best if i take the 2 out huh

Answer 28

pull it out! make u=x and dv=sinx

Answer 29

yes! make thing easier! alway s think about an easier method

Answer 30

so v=-cosx

Answer 31

correct!

Answer 32

ok so

Answer 33

now you will see that it is done already just make sure you add all what we did together

Answer 34

\[x^2sinx-2[-xcosx-\int\limits_{}^{}-cosxdx]\]

Answer 35

is that right what i did with the 2? put everything after it in brackets?

Answer 36

Correctt -2 is a factor to all of that second part

Answer 37

ok so final answer

Answer 38

\[x^2sinx+2xcosx+2sinx+C\]

Answer 39

you missed a negative sign should be -2sinx

Answer 40

oh yeah i see it now thank you

Answer 41

everything else is good!
and you are welcome

Answer 42

in integration by part pay real attention to details you might forgot things
so when you clean up the miss return to your work and see if that's true! comprend!

Answer 43

i checked by differentiating it and all is clean and good!
YaY

Answer 44

mess* (correction)