Question

find \\( \int \left(6x^4 + 5x^6\
ight) dx \\) \\( + c \\)

Explanation:

Step1: Split the integral

$\int (6x^4 + 5x^6) dx = \int 6x^4 dx + \int 5x^6 dx$

Step2: Apply power rule to first term

$\int 6x^4 dx = 6 \cdot \frac{x^{4+1}}{4+1} = \frac{6}{5}x^5$

Step3: Apply power rule to second term

$\int 5x^6 dx = 5 \cdot \frac{x^{6+1}}{6+1} = \frac{5}{7}x^7$

Step4: Combine the results

Add the two antiderivatives together.

Answer:

$\frac{6}{5}x^5 + \frac{5}{7}x^7$