Specialist2024 NHT Exam 2 Section A · Q11CAS active1 mark

Reduction formula for an integral with a logarithm

If $I_n = \int_1^e x^2 \left(\log_e x\right)^n dx$ where $n \in N$ , then for $n \geq 2$ , $I_n$ is equal to

1 mark

-\frac{n}{3} I_{n-1}

\frac{x^3 \left(\log_e x\right)^n}{3} - \frac{n}{3} I_{n-1}

\frac{e^3}{3} - \frac{1}{3} I_{n-1}

\frac{e^3}{3} - \frac{n}{3} I_{n-1}

\frac{e^3}{3} - \frac{1}{3} - \frac{n}{3} I_{n-1}

Hints, answer checking and worked solutions come with a Season Pass.