question 20 · 1 point evaluate the indefinite integral given below. provide your answer below: $int…

Explanation:

Step1: Use substitution method

Let $u = - 6x^{5}-2$, then $du=-30x^{4}dx$, and $x^{4}dx=-\frac{1}{30}du$. The integral $\int4x^{4}e^{-6x^{5}-2}dx$ becomes $\int4\times(-\frac{1}{30})e^{u}du$.

Step2: Simplify the integral

$\int4\times(-\frac{1}{30})e^{u}du=-\frac{2}{15}\int e^{u}du$.

Step3: Integrate $e^{u}$

Since $\int e^{u}du = e^{u}+C$, then $-\frac{2}{15}\int e^{u}du=-\frac{2}{15}e^{u}+C$.

Step4: Substitute back $u$

Substitute $u = - 6x^{5}-2$ back, we get $-\frac{2}{15}e^{-6x^{5}-2}+C$.

Answer:

$-\frac{2}{15}e^{-6x^{5}-2}+C$