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xsqrt(1+2x^(2))...

`xsqrt(1+2x^(2))`

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To solve the integral \( \int x \sqrt{1 + 2x^2} \, dx \), we will follow these steps: ### Step 1: Substitution Let \( t = 1 + 2x^2 \). Then, we differentiate \( t \) with respect to \( x \): \[ dt = 4x \, dx \quad \Rightarrow \quad dx = \frac{dt}{4x} \] From the substitution, we can express \( x \, dx \) as: ...
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