Integration by substitution
General
Grade 12
Question:
Find $\int (4x+6)\sqrt{2x^2+6x+5} dx$
Step-by-Step Solution
Key Concept: General
Let $2x^2 + 6x + 5 = t \Rightarrow (4x + 6)dx = dt$<br>$\therefore \int (4x+6)\sqrt{2x^2+6x+5} dx = \int \sqrt{t} dt = \frac{t^{3/2}}{3/2} + C = \frac{2}{3}(2x^2 + 6x + 5)^{3/2} + C$
Correct Answer: $\frac{2}{3}(2x^2 + 6x + 5)^{3/2} + C$