Question Detail

To integrate a polynomial, apply the power rule for integration term by term: ∫x&supn; dx = x&supn;¹/(n+1) + C.

• ∫4x³ dx = 4 * (x³¹/(3+1)) = 4 * (x&sup4;/4) = x&sup4;
• ∫3x dx = 3 * (x¹¹/(1+1)) = 3 * (x²/2) = (3/2)x²
• ∫-1 dx = -x

Combining these terms, the indefinite integral is x&sup4; + (3/2)x² - x + C. Option B matches this result (without the arbitrary constant C, which is common in multiple-choice questions).