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Evaluate the indefinite integral:

Make a trigonometric substitution:

so the integral (i) becomes


Now, substitute back for t = arcsin(x²), and you finally get the result:

✔
________
You could also make
x² = cos t
and you would get this expression for the integral:

✔
which is fine, because those two functions have the same derivative, as the difference between them is a constant:
![\mathsf{\dfrac{1}{2}\,arcsin(x^2)-\left(-\dfrac{1}{2}\,arccos(x^2)\right)}\\\\\\ =\mathsf{\dfrac{1}{2}\,arcsin(x^2)+\dfrac{1}{2}\,arccos(x^2)}\\\\\\ =\mathsf{\dfrac{1}{2}\cdot \left[\,arcsin(x^2)+arccos(x^2)\right]}\\\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{\pi}{2}}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5C%2Carcsin%28x%5E2%29-%5Cleft%28-%5Cdfrac%7B1%7D%7B2%7D%5C%2Carccos%28x%5E2%29%5Cright%29%7D%5C%5C%5C%5C%5C%5C%0A%3D%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5C%2Carcsin%28x%5E2%29%2B%5Cdfrac%7B1%7D%7B2%7D%5C%2Carccos%28x%5E2%29%7D%5C%5C%5C%5C%5C%5C%0A%3D%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cleft%5B%5C%2Carcsin%28x%5E2%29%2Barccos%28x%5E2%29%5Cright%5D%7D%5C%5C%5C%5C%5C%5C%0A%3D%5Cmathsf%7B%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B%5Cpi%7D%7B2%7D%7D)

✔
and that constant does not interfer in the differentiation process, because the derivative of a constant is zero.
I hope this helps. =)
<span>$16,000 / (100% - 20%) = $16,000 / .8 = $20,000
to verify, work the answer backwards.
$20,000 - $20,000 * 20% = $20,000 - $4,000 = $16,000
</span>
Step-by-step explanation:
substitute 2 into x
1. (u ○ w)(2)
u(w(x))
= 4(-5x+1)+2
= 4(-5.2+1)+2
= 4(-9)+2
=-34
2. (w ○ u)(2)
w(u(x))
= -5(4x+2)+1
= -5(4.2+2)+1
= -5(10)+1
= -49
Answer:
z = 8
Step-by-step explanation:
3/4 (z+4)=9
3/4z + 3 = 9
3/4z = 6
z = 8
Answer:

Step-by-step explanation:
From the definition if inverse function we can say if y = f(x) and x = h(y) then h(x) is the inverse function of f(x).
Here the given function is
and we have to find the
i.e. the inverse function of g(x).
Now, let us assume
Now, taking ln both sides we get,
{Since
}
⇒
Therefore,
(Answer)