If dy/dx = 3x^5 + 6e^2x, what is y?
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We'll re-write the given expression, isolating dy:
dy = (3x^5 + 6e^2x)dx
We'll integrate both sides:
Int dy = Int (3x^5 + 6e^2x)dx
We'll use the property of integral to be additive:
Int dy = Int 3x^5dx + Int 6e^2xdx
Int dy =3x^6/6 + 6e^2x/2+ C
Int dy =x^6/2 + 3e^2x+ C
But Int dy = y, therefore y = x^6/2 + 3e^2x+ C, where C represents a constant.
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