Question

Evaluate the integral ∫(17(x - 1)(x² + 16)) dx. (Remember to use absolute values where appropriate. Use C for the constant of integration.)

Answer 1

To evaluate the integral ∫(17(x - 1)(x² + 16)) dx, expand and distribute the expression. Then, integrate each term individually and apply the power rule for integration to simplify the expression.

Step-by-step explanation:

To evaluate the integral ∫(17(x - 1)(x² + 16)) dx, we need to expand the expression and distribute.

Step 1: Distribute 17 into (x - 1)(x² + 16):

∫(17x³ + 272x - 17x² - 272) dx

Step 2: Integrate each term individually:

∫17x³ dx + ∫272x dx - ∫17x² dx - ∫272 dx

Step 3: Apply the power rule for integration:

&frac;17×&frac;14x⁴ + &frac;272×&frac;12x² - &frac;17×&frac;13x³ - 272x + C

Simplifying the expression: &frac;221×x⁴ + 136x² - &frac;17×x³ - 272x + C