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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