use substitution to find the indefinite integral.\n int 10(3x - 1)^{9} dx \n int 10(3x - 1)^{9} dx=square

Explanation:

Step1: Set the substitution

Let $u = 3x - 1$. Then $du=3dx$, and $dx=\frac{1}{3}du$.

Step2: Rewrite the integral

The integral $\int 10(3x - 1)^9dx$ becomes $\int 10u^9\times\frac{1}{3}du=\frac{10}{3}\int u^9du$.

Step3: Integrate with respect to u

Using the power - rule for integration $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$), we have $\frac{10}{3}\times\frac{u^{10}}{10}+C=\frac{1}{3}u^{10}+C$.

Step4: Substitute back u

Substitute $u = 3x - 1$ back into the result. We get $\frac{1}{3}(3x - 1)^{10}+C$.

Answer:

$\frac{1}{3}(3x - 1)^{10}+C$