a) \int (5s^2 - 3 \cos x) dx

c) \int e^{x+y} dx

Question

a) \int (5s^2 - 3 \cos x) dx

c) \int e^{x+y} dx

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Indefinite Integrals", "Integration with Respect to x" ], "current_concepts": [ "Indefinite Integrals", "Integration with Respect to x", "Constant of Integration" ] } ## Integrate part a with respect to x $$ \begin{aligned} \int (5s^2 - 3\cos x) \, dx &= \int 5s^2 \, dx - \int 3\cos x \, dx \ &= 5s^2 x - 3\sin x + C \end{aligned} $$ ## Integrate part c with respect to x $$ \begin{aligned} \int e^{x+y} \, dx &= \int e^y \cdot e^x \, dx \ &= e^y \int e^x \, dx \ &= e^y \cdot e^x + C \ &= e^{x+y} + C \end{aligned} $$ ## Question a $$ 5s^2 x - 3\sin x + C $$ ## Question c $$ e^{x+y} + C $$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Calculus", "Indefinite Integrals" ] }

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Question

Explanation:

Integrate part a with respect to x

Integrate part c with respect to x

Answer:

Question a

Question c