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To integrate e^(-2x)dx, you need to take a u substitution.
u=-2x
du=-2dx
Since the original integral does not have a -2 in it, you need to divide to get the dx alone.
-(1/2)du=dx
Since the integral of e^x is still e^x, you get:
y = -(1/2)e^(-2x)
Well, that was one method. I usually solve easier functions like this by thinking how the function looked like before it was differentiated. I let f(x) stand for the given function and F(x) stand for the primitive function; the function we had before differentiation (the integrated function).
f(x)= e-2x <-- our given function
F(x)= e-2x/-2 <-- our integrated function
Evidence: F'(x)= -2e-2x/-2 = e-2x = f(x) Q.E.D
It's as simple as that.
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How do you integrate x power x?
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use the double angle formula for cos(2x) which is: cos(2x)=2cos^2(x)-1 by this relation cos^2(x)=(cos(2x)+1)/2 now we'd integrate this instead this will give sin(2x)/4+x/2 =) hope this helps
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What is the second derivative of xsqaured e to the power of x?
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e 2x = (1/2) e 2x + C ============
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int[e(2X) +e(- 2X)] integrate term by term 1/22 e(2X) - 1/22 e(- 2X) + C (1/4)e(2X) - (1/4)e(- 2X) + C ====================
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2x
How do you integrate e-2x?
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How do you integrate of e -2x for x0?
The integral of e-2x is -1/2*e-2x + c but I am not sure what "for x0" in the question means.
How do you integrate e power minus 2x?
∫e^(-2x) dx Let u = 2x du= 2 dx dx=(1/2) du ∫e^(-2x) dx = (1/2) ∫e^-u du = (1/2) (-e^-u) = -e^-u /2 + C = -e^-(2x) / 2 + C
How do you integrate functions?
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
How to integrate of e to the power of -2x with x to the power of 2?
e-2x^2 cannot be integrated, only approximated unless there is an additional x attached to the front of the e, otherwise this function is not integrable Actually, it can be integrated, but it requires multivariable calculus and a conversion from cartesian to polar form to do so.
How you integrate xxxx 1 dx?
.2x^5+x+C
What is the integral of 2-2x with limits 0 to t?
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D dx e 2x?
d/dx(e^2x) = 2xe^2x
How do you integrate problems in calculus by substitution?
You would use something called u substitution for example if you are integrating a problem like 4x(2x^(2)) dx your u would equal 2x^(2) then you would take the derivative of your u, which would make it 4x By doing this the 4x disappears in the problem and you can integrate you would keep the 2x^(2) in u form and integrate the u as if it was an x which would give you (u)^(2)/2 then just plug back the 2x^(2) into u.
