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int(x^3)/(x+1)\ dx is equal to x+(x^2)/2...

`int(x^3)/(x+1)\ dx` is equal to `x+(x^2)/2+(x^3)/3-log|1-x|+C` (b) `x+(x^2)/2-(x^3)/3-log|1-x|+C` (c) `x-(x^2)/2-(x^3)/3-log|1+x|+C` (d) `x-(x^2)/2+(x^3)/3-log|1+x|+C`

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To solve the integral \( \int \frac{x^3}{x+1} \, dx \), we can start by simplifying the integrand using polynomial long division. ### Step 1: Polynomial Long Division We divide \( x^3 \) by \( x + 1 \): 1. Divide the leading term: \( x^3 \div x = x^2 \). 2. Multiply \( x^2 \) by \( x + 1 \): \( x^2(x + 1) = x^3 + x^2 \). 3. Subtract from \( x^3 \): ...
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