Question

how do i integrate ucos(u)?

Answer 1

i dont know how to integrate anything which is timed together, how do I?

I haven't done anything to do with int by parts yet

Answer 2

can i just do the integral of the u and the integral of the cos(u) and times them together?

Answer 3

integration by parts
do you know it?

Answer 4

no, doing it next lesson

Answer 5

so i don't need it for this homework that I am doing

Answer 6

and by the way\[\int f(x)g(x)dx\neq\int f(x)dx\cdot\int g(x)dx\]that is a criticalo thing to know

Answer 7

critical*

Answer 8

aaaawwww :(, thats simple though lol

Answer 9

but then we would never need u-substitutions now would we?
;)

Answer 10

life would be so mch easier for me if there was no need for the u substitutions at the moment lol

Answer 11

can the question be done without int by parts then?

Answer 12

the start question was integrate xcos(x^2) using the substitution u=u^2

Answer 13

I'm going to say no, though I have been known to be wrong once or twice :)

Answer 14

-but
the integral you just wrote can be done without integration by parts

Answer 15

you have the wrong u-sub\[\int x\cos(x^2)dx\]\[u=x^2\]so what is du ?

Answer 16

2x(dx)?

Answer 17

right, so what is our integral now?

Answer 18

how about if I write it like this?\[\int x\cos(x^2)dx=\int\cos(x^2)(xdx)\]then we have\[u=x^2\implies du=2xdx\]so we are going to sub\[xdx=\frac12du\]

Answer 19

\[1/2\int\limits_{}^{}\cos(x^{2}) .du\]?

Answer 20

almost, but you forgot to sub u=x^2

Answer 21

1/2 int cos(u) .du

Answer 22

there we go :)

Answer 23

:)

Answer 24

therefore, the answer is:

1/2sin(x^2) ?

Answer 25

don't forget +C
but, yes

Answer 26

i always forget the constant lol :)

Answer 27

thank you so much for your help, you have been insanely helpful :D

Answer 28

the funny thing is you pretty much don't need it until you take differential equations, at which point it is essential

you are welcome, see you around :D