Indefinite Integration
Complex Expressions
Grade 12
Question:
<p>The value of $\displaystyle \int \frac{e^x + x^4 + 2}{(1+x^2)^{5/2}} dx$ is equal to</p>
<p>(A) $\frac{e^x(x+1)}{(1+x^2)^{3/2}} + C$</p>
<p>(B) $\frac{e^x(1+x+x^2)}{(1+x^2)^{3/2}} + C$</p>
<p>(C) $\frac{e^x(1+x)}{(1+x^2)^{3/2}} + C$</p>
<p>(D) none of these</p>
Step-by-Step Solution
Key Concept: Recognize that the numerator matches the derivative pattern of the denominator raised to a fractional power
<p>This integral combines exponential and polynomial functions over a power of a quadratic expression. Use integration by parts or recognize the pattern of derivative of a quotient.</p>
Correct Answer: B