Question 10:
Find the integration using Substitution Method.
(3 marks)
\[
\int x\left(3 x^{2}+5\right)^{3} d x
\]

Answer

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Answer

Evaluate the integral: \(\frac{1}{6}\left(\frac{1}{4}u^4+C\right)\)

Steps

Step 1 ：Let \(u = 3x^2 + 5\), then \(du = 6xdx\)

Step 2 ：Substitute in the given integral: \(\int\frac{1}{6}u^3du\)

Step 3 ：Evaluate the integral: \(\frac{1}{6}\left(\frac{1}{4}u^4+C\right)\)