# Antiderivative of 6e^x and 4x^2

1. May 24, 2010

### eclar56

antiderivative of 6e^x and 4x^2

--> 6e^x
-->1/6e^x??

--> 4x^2
--> 2x^3??

2. May 24, 2010

### n.karthick

Could you tell the steps you followed to find anti-derivative of $4x^2$ and how you got the answer.

3. May 24, 2010

### eclar56

4x^2:
One of the teachers said today to add one to the power, and divide whats out front by what the power was. So 4/2 = 2, and 2 + 1 = 3..

4. May 24, 2010

### n.karthick

Oh no! As far as adding one to the power is ok, but could you re-call correctly what has been told about the divisor.
You can refer to standard integrals in the PF library to know the integration of $x^n$.

5. May 24, 2010

### eclar56

Ok I think I figured it out. Thanks heaps for helping anyway. Don't know what my teacher was talking about but!! Still don't know the 6e^x one but..

6. May 24, 2010

### HallsofIvy

The derivative of Cf(x), where C is a constant, is Cf'(x) so $(6e^x)'= 6(e^x)'$. Do you know what the derivative of $e^x$ is?

7. May 24, 2010

### eclar56

It's just itself. So the whole thing is just the same? It's still just 6e^x..?

8. May 24, 2010

### Lancelot59

Yes. Remember what happens when you derive something with a constant in front of it? You pull the constant out:

$$\frac{d}{dx} 6e^{x}$$
$$6\frac{d}{dx} e^{x}$$
$$6(e^{x})$$

The function exdoesn't change when you derive it unless you have something other than x in the exponent and have to use the chain rule.

9. May 24, 2010

### mg0stisha

don't forget your constant of integration, but yes.

10. May 24, 2010

### Lancelot59

$$\int{6e^{x}} dx =6\int{e^{x}} dx = 6e^{x} + c$$