#Evaluating an Integral
white pier
open grove
yeah, use IBP
i wud take 4x=t
to not make stuff complicated
then use IBP considering, arcsin(t) as the first function, 1 as the 2nd function
desert yoke
,w d/dx arcsin(x)
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desert yoke
^
steady smelt
it's a standard derivative
desert yoke
1 was the dv so you have to integrate not derive
wet pond
Yes thats right
But notice how g'(x) is in the integral, and from there you have to find g(x)
Here, you calculated g'(x) after finding g(x) in the integral
Wait
No i messed up
Well you did
Idk your work is confusing
desert yoke
g(x) and g’(x) were fine but f’(x)=1 so to get f(x) you have to integrate
wet pond
Either way, just say g'(x) = 1 and f(x) = arcsin(4x)
Because then you would have g'(x) = arcsin(4x)
And finding the antiderivative of that is just finding the original integral
desert yoke
It comes from your formula too, one is normal f(x) and other is g’(x)
You’re using backwards notation from the picture you sent, f(x) = arcsin(4x) and f’(x)= 4/ sqrt(1-16x^2)
And g’(x)=1 so what is g(x)
Yes
Now put those values in your formula
wet pond
$$\int 1x \times \frac 4{\sqrt{1 - 16x^2}} \dd{x}$$
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King Leo [Ping For Help]
wet pond
And you evaluated this as 4arcsin(4x)?
Thats not right
Make a substitution for 1 - 16x^2
$$u = 1 - 16x^2$$
$$\dd{u} = \cdots$$
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King Leo [Ping For Help]
wet pond
And you can slightly modify [this integral](#1337999545153486848 message)
You need to make a u-substitution to solve this
No
Can you show how you got that
Oh wait
Is this just for du = ...
So whats your new integral
Should be negative
?
I gtg
desert yoke
[ $\int \arcsin(4x)dx$ \ $u=\arcsin(4x),du=\frac{4}{\sqrt{1-16x^2}}$ \ $dv=1, v=x$\ $x\arcsin(4x)-\int \frac{4x}{\sqrt{1-16x^2}}dx$]
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alexplqys
Compile Error! Click the 
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desert yoke
[$u=1-16x^2,du=-32xdx \implies \frac{-1}{8}du=4xdx$ ]
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alexplqys
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
desert yoke
[\int \frac{du}{-8\sqrt{u}}]
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alexplqys
desert yoke
,w integrate 1/(8sqrt(x)) dx
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desert yoke
It’s correct