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Sticky Note
What is the value of the integral ∫ e^(x² + ln x) dx ?
  1. (1/2) e^(x²)
  2. e^(x² + x)
  3. x·e^(x²)
  4. None of these
Explanation

What is the value of the integral:

Step 1: Simplify the integrand

Recall:

So,

Step 2: The integral becomes:

Now use substitution:

Let u = x^2 Rightarrow du = 2x , dx Rightarrow frac{1}{2} du = x , dx

So,


int x cdot e^{x^2} , dx = frac{1}{2} int e^u , du = frac{1}{2} e^u + C = frac{1}{2} e^{x^2} + C

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