use the substitution method to find the indefinite integral. what expression should be used for the…

use the substitution method to find the indefinite integral. what expression should be used for the substitution, u?\na. 3x\nb. x³ - 3\nc. x\nd. x³\nfind the indefinite integral.\n∫3x²(x³ - 3)dx = \n∫3x²(x³ - 3)dx = \nfind the indefinite integral without using substitution.\n∫3x²(x³ - 3)dx = □

use the substitution method to find the indefinite integral. what expression should be used for the substitution, u?\na. 3x\nb. x³ - 3\nc. x\nd. x³\nfind the indefinite integral.\n∫3x²(x³ - 3)dx = \n∫3x²(x³ - 3)dx = \nfind the indefinite integral without using substitution.\n∫3x²(x³ - 3)dx = □

Answer

Explanation:

Step1: Recall substitution rule

If (u = x^{3}-3), then (du=3x^{2}dx).

Step2: Apply substitution

(\int3x^{2}(x^{3} - 3)dx=\int udu).

Step3: Integrate (\int udu)

Using the power rule (\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C(n\neq - 1)), for (n = 1), (\int udu=\frac{u^{2}}{2}+C).

Step4: Substitute back (u=x^{3}-3)

(\frac{(x^{3}-3)^{2}}{2}+C).

Answer:

(\frac{1}{2}(x^{3}-3)^{2}+C)