Question

indefinite integral of 4x^3 sinx^4 dx

Answer 1

\[\Large \int\limits \sin \color{#F35633}{x^4}\left(4x^3\;dx\right)\]We'll apply a u-substitution.
We want to make \(\Large \color{#F35633}{\text{this part}}\) our u.
Do you understand how to find du?

Answer 2

du=(4x^3)dx right? @zepdrix

Answer 3

Yes, good :)

Answer 4

Confused on how to apply the substitution?
I tried to group the other part in brackets so it'd be easier to line things up.

Answer 5

so sin(u)du right?? @zepdrix

Answer 6

\[\Large \int\limits \sin u (du)\]Yes, good! :)

Answer 7

then I get the derivative of sin(

Answer 8

then I get the derivative of sin(u) right?? @zepdrix

Answer 9

yes

Answer 10

cos(u)du right?? @zepdrix

Answer 11

When we integrate, the swirly S bar `and` the differential du will both disappear as a part of that process.

So when your sin(u) changes, the du should disappear along with the bar.
But I think you maybe have your derivatives confused! :O

Derivative of sinu = cosu
Integral of sinu should give us -cosu, yes? :)

Answer 12

yes!:) you confused me on the beginning :O @zepdrix

Answer 13

ah, my bad :3

Answer 14

ok wait, nvm I get it :p the du no longer exists because it canceled right? :) @zepdrix

Answer 15

Well, why does this \(\LARGE \int\) no longer exist? :O

Answer 16

because it goes away with the du right?? @zepdrix

Answer 17

yes :x I was just a little confused when you said "canceled" lol

Answer 18

sorry so then I have -cos(u) which its gonna be -cos(x^4) right ?? @zepdrix

Answer 19

Yay good job \c:/

Answer 20

We would probably want to throw a +C onto the end to include the entire family of solutions since it's an `indefinite` integral.

Answer 21

so my answer is -cos(x^4) +c ?? @zepdrix

Answer 22

Yes! :)

Answer 23

thank you!! you should help me more often!!!:} @zepdrix