Question

find \\( \int (7x^7 + 5x^6) \\, dx \\)

Explanation:

Apply the sum rule for integration

$$ \int (7x^7 + 5x^6) \, dx = \int 7x^7 \, dx + \int 5x^6 \, dx $$

Apply the power rule for integration

$$ \int x^n \, dx = \frac{x^{n+1}}{n+1} \quad (n eq -1) $$

$$ \int 7x^7 \, dx = 7 \cdot \frac{x^8}{8} = \frac{7}{8}x^8 $$

$$ \int 5x^6 \, dx = 5 \cdot \frac{x^7}{7} = \frac{5}{7}x^7 $$

Combine the terms

$$ \int (7x^7 + 5x^6) \, dx = \frac{7}{8}x^8 + \frac{5}{7}x^7 + C $$

Answer:

Find \(\int (7x^7 + 5x^6) \, dx\)

<blank>\(\frac{7}{8}x^8 + \frac{5}{7}x^7\)</blank> \(+ C\)