question 14 - 1 point evaluate the indefinite integral given below. provide your answer below: $int…

Explanation:

Step1: Use substitution

Let $u = 5x^{4}+10$, then $du=20x^{3}dx$, and $x^{3}dx=\frac{1}{20}du$. The integral $\int - 7x^{3}\cos(5x^{4}+10)dx$ becomes $\int-7\times\frac{1}{20}\cos(u)du$.

Step2: Integrate with respect to u

$\int-\frac{7}{20}\cos(u)du=-\frac{7}{20}\sin(u)+C$.

Step3: Substitute back u

Substitute $u = 5x^{4}+10$ back into the result, we get $-\frac{7}{20}\sin(5x^{4}+10)+C$.

Answer:

$-\frac{7}{20}\sin(5x^{4}+10)+C$