A curve has gradient e(power 4x)+e(power -x) at the point (X,Y). Given that the curve passes through the point (0,3), find the equation of the curve.
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The integration in question uses . If you don't know why this is the case you'll need to use a textbook or ask your teacher for some more tuition and/or examples on integration
Well, the most basic thing about integration is that it is, up to a constant, the inverse of differentiation. Let's say I take the function f(x) = sin(x), and I differentiate it to obtain f'(x) = cos(x). Well now, I can integrate it to get back to my original function:
Notice the constant there. So use the antiderivative that e^(i*pi) just gave you, plus this fact, and then use the constant of integration to make your curve go through the desired point. Does that make sense?