Evaluate the integral using Integration by Parts. $$ \int 7 \sin^{-1} (x) dx $$ (Express numbers in exact form. Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) $$ \int 7 \sin^{-1} (x) dx = 7x \sin^{-1} (x) + 7\sqrt{1-x^2} + C $$
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The formula for integration by parts is $\int u \, dv = uv - \int v \, du$. Step 2: Choose u and dv. Let $u = 7 \sin^{-1} (x)$ and $dv = dx$. Step 3: Find du and v. Differentiate u to find du: $du = \frac{d}{dx} (7 \sin^{-1} (x)) dx = 7 \cdot Show more…
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