How do you find the indefinite integral of #int arcsin x ^2dx#?
Aurora AlvaradoThis is not possible with elementary functions.
Therefore, you should stick to definite integrals of this integrand in elementary calculus.
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To find the indefinite integral of (\int \arcsin(x^2) , dx), you can use integration by parts. Let (u = \arcsin(x^2)) and (dv = dx). Then, (du = \frac{1}{\sqrt{1-x^4}} \cdot 2x , dx) and (v = x). Apply integration by parts formula: (\int u , dv = uv - \int v , du). After substituting the values, simplify the resulting integral and solve it.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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