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int_(0)^(1)(xdx)/(sqrt(x^(4)+1))=

$\int_{0}^{1}\frac{x\,dx}{\sqrt{x^{4}+1}}=$

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Evaluate definite integrals using the chain rule

Full solution

Q.

\int_{0}^{1}\frac{x\,dx}{\sqrt{x^{4}+1}}=

Set up the integral: Set up the integral. $\newline$ We need to evaluate $\int_{0}^{1}\frac{x\,dx}{\sqrt{x^{4}+1}}$ .
Consider substitution: Consider substitution. $\newline$ Let $u = x^4 + 1$ , then $du = 4x^3 dx$ . $\newline$ However, we have $x dx$ in the integral, not $x^3 dx$ , so this substitution isn't directly applicable.
Evaluate the integral directly: Evaluate the integral directly. $\newline$ Since a simple substitution doesn't work, we evaluate the integral as it is: $\newline$ $\int_{0}^{1}\frac{x\,dx}{\sqrt{x^{4}+1}}$ . $\newline$ This integral does not simplify easily with elementary functions and might require numerical methods or special functions for exact evaluation.

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