Differentiate and then integrate: x^2 + 3x
To differentiate, the rule is to bring the power down to the front and multiply the expression, then take one off the value of the power, for example: d/dx(x2) = (2)x2-1 = 2x, so the answer to the the question given is: (2)x2-1 + (1)3x1-1 = 2x + 3
To integrate, you first add one to the power, and then divide the expression by the new value of the power for example: integrate(x2) = x2+1(1/3)So the answer to the question is: x2+1(1/3) + 3x1+1(1/2) = (1/3)x3 + (1/2)x2 + CRemember to add the constant of integration (C) and sometimes if we were to differentiate just a number, the expression would disappear and so we need to account for this in the integral.
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