| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2022 |
| Session | January |
| Marks | 4 |
| Topic | Standard Integrals and Reverse Chain Rule |
| Type | Integrate after simplifying a quotient |
| Difficulty | Moderate -0.3 This question requires algebraic manipulation (splitting the fraction and simplifying powers) followed by standard integration using the power rule. While it involves multiple steps, each step is routine: rewrite as separate terms with negative/fractional powers, integrate term-by-term, and simplify. This is slightly easier than average as it's a straightforward application of standard techniques with no conceptual challenges or problem-solving required. |
| Spec | 1.08b Integrate x^n: where n != -1 and sums |
4. Find
$$\int \frac { 2 x ^ { 2 } + 6 x - 5 } { 3 \sqrt { x ^ { 3 } } } d x$$
simplifying your answer.\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM 2022 Q4 [4]}}