Question

integrate 5x cube minus sin3x

Answer 1

\[\int\limits ((5x)^3-\sin(3x))dx\] you mean that?

Answer 2

well if that's what you mean you can make 2 integrals out of it and just integrate the left part and then the right part of it. need more help?

Answer 3

Yes I do

Answer 4

well now we have \[\int\limits (5x)^3 dx - \int\limits \sin(3x) dx\]

well, ... i could write it out now for you but maybe you can remember some rules about integrating and that will help you. i can calculate it for you but that would not help you much i guess.

Answer 5

\[5 \int\limits x^3 dx - \int\limits \sin(3x) dx\]

now just think of what equation you have to build the derivate of to get x^3 and sin 3x

Answer 6

x raised to power four over 4

Answer 7

right

Answer 8

that's right so we have the left side with \[\frac{125x^4}{ 4 }\] (i forgot the 5^3 before)

and what about the right side? what is the derivate of sinus?

Answer 9

am going to guess here

Answer 10

minus cos

Answer 11

sinus --> cosinus --> minus sinus --> minus cosinus --> sinus ( the loop begins anew)

so you have sin(3x) that means before that you hade a minus cosinus. therefore what is the solution for the right side?

Answer 12

plus cosx

Answer 13

plus cos3x

Answer 14

good but there is something missing. what happens if you build the derivate of the equation you just wrote? you get:\[-3\sin(3x)\]
so you need to divide it with 3
and the whole endresult is:
\[\int\limits ((5x)^3-\sin(3x) ) dx = \frac{125x^4} {4} + \frac{\cos(3x)}{3}\]

Answer 15

why divide by 3

Answer 16

was 3x diffrentiated

Answer 17

actually we divided cos 3x by 3 because while taking differential we get multiplied by 3

Answer 18

http://en.wikipedia.org/wiki/Chain_rule

that explains the /3

Answer 19

simply differentiate cos 3x/3 you will get back -sin 3x

Answer 20

chain rule

Answer 21

indeed

Answer 22

so integrate cos3x and divide by diffrention of 3x

Answer 23

is that it

Answer 24

well yes, but i wouldn't call it like that. just: but it's fine :)

Answer 25

Thank you