Science Quiz / Calculus Challenge

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Can you name the solutions to these differential and integral equations?

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d/dx(sin(x))Trigonometric function
∫ x dxDon't forget the constant!
d/dx(x²-x⁻¹+3)Basic stuff
∫ 3x²-4x+5 dxDon't forget the constant!
dy/dt=yMulitplicative constant is 'A'
d/dx(tan(x))Trigonometric function
d/dx(xˣ)The log function proves useful..
∫2sin(x)cos(x)dxIn terms of one trigonometric function (and constant)
d/dx(arcsin(x))Write 'root' for sqrt
∫1/√(x²+1) dxHyperbolic (not in terms of 'e')
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