Indefinite Integration

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Evaluate the indefinite integral: $\int \frac{x}{\sqrt{1-x^4}} \, dx$

\arcsin(x^2) + C

\frac{1}{2}\arcsin(x^2) + C

\frac{1}{4}\arcsin(x^2) + C

\frac{1}{2}\arcsin(x^4) + C

Evaluate the indefinite integral: $\int \frac{x^2}{\sqrt{x^2+4}} \, dx$ .

\frac{x^2\sqrt{x^2+4}}{2} - 2\ln\left|x+\sqrt{x^2+4}\right|+C

\frac{\sqrt{x^2+4}}{2} - 2\ln\left|x+\sqrt{x^2+4}\right|+C

\frac{x\sqrt{x^2+4}}{2} + 2\ln\left|x+\sqrt{x^2+4}\right|+C

\frac{x\sqrt{x^2+4}}{2} - 2\ln\left|x+\sqrt{x^2+4}\right| + C

Determine the indefinite integral: $\int \frac{\sqrt{1 - x^2}}{x^4} \, dx$

\frac{(1-x^2)^{3/2}}{3x^3} + C

\frac{\sqrt{1-x^2}}{3x^3} + C

-\frac{\sqrt{1-x^2}}{x^3} + C

-\frac{(1-x^2)^{3/2}}{3x^3} + C

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