Question

Find the integral: \[ \int x^m \cdot x^n \, dx \]

• A. \( \frac{x^{m+n+1}}{m+n+2} + k \)
• B. \( \frac{x^{m+n}}{m+n} + k \)
• C. \( \frac{x^{m+n+1}}{m+n+1} + k \)
• D. \( (m+n) x^{m+n-1} + k \)

Hint:

When multiplying powers of \( x \), add the exponents before integrating.

Answer 1

The Correct Option is C

The given integral is \( \int x^m \cdot x^n \, dx \). First, simplify the integrand: \[ x^m \cdot x^n = x^{m+n}. \] Now, integrate \( x^{m+n} \): \[ \int x^{m+n} \, dx = \frac{x^{m+n+1}}{m+n+1} + k. \] Thus, the correct answer is option (C).