Integration by substitution
General
Grade 12
Question:
Find $\int \frac{9x^2+2}{3x^3+2x+10} dx$
Step-by-Step Solution
Key Concept: General
Put $3x^3 + 2x + 10 = t \Rightarrow (9x^2 + 2)dx = dt$<br>$\therefore \int \frac{9x^2+2}{3x^3+2x+10} dx = \int \frac{dt}{t} = \ln|t| + C = \ln(3x^2 + 2x + 10) + C$<br>Note : $\ln|3x^2 + 2x + 10|$ is not used above as $3x^2 + 2x + 10 > 0 \forall x \in R$
Correct Answer: $\ln(3x^2 + 2x + 10) + C$