题目
题目

MCD2130 - T2 - 2025 MCD2130 Test 3

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Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(10x+5)5x2+5x+5]\displaystyle\int{\left(10\,x+5\right)\,\sqrt{5\,x^2+5\,x+5}} [math: dx] . [math: u=] [input] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(10x+5)5x2+5x+5]\displaystyle\int{\left(10\,x+5\right)\,\sqrt{5\,x^2+5\,x+5}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 19

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思路分析
The problem presents a step-by-step substitution scenario for integrating a product involving a square root. I will address each blank in order and explain why the supplied fillings are appropriate. a) Choose an appropriate substitution, u, to find the integral ∫(10x+5)√(5x^2+5x+5) dx. - Provided fill: u = 5x^2 + 5x + 5 - Rationale: When you see an integrand of the form (derivative of something) times a function of that same something......Login to view full explanation

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Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(10x+2)5x2+2x+7]\displaystyle\int{\left(10\,x+2\right)\,\sqrt{5\,x^2+2\,x+7}} [math: dx] . [math: u=] [input] Your last answer was interpreted as follows: [math: 5x2+2x+7] 5\,x^2+2\,x+7 The variables found in your answer were: [math: [x]] \left[ x \right] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(10x+2)5x2+2x+7]\displaystyle\int{\left(10\,x+2\right)\,\sqrt{5\,x^2+2\,x+7}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 19

Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(15x2+5)5x3+5x+5]\displaystyle\int{\left(15\,x^2+5\right)\,\sqrt{5\,x^3+5\,x+5}} [math: dx] . [math: u=] [input] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(15x2+5)5x3+5x+5]\displaystyle\int{\left(15\,x^2+5\right)\,\sqrt{5\,x^3+5\,x+5}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 2

Question texta) Choose an appropriate substitution, [math: u], to find the integral [math: ∫(15x2+2)5x3+2x+7]\displaystyle\int{\left(15\,x^2+2\right)\,\sqrt{5\,x^3+2\,x+7}} [math: dx] . [math: u=] [input] b) Find [math: dudx]\displaystyle \dfrac{du}{dx}. [math: dudx=]\displaystyle \dfrac{du}{dx}=[input] c) Hence, find the integral [math: ∫(15x2+2)5x3+2x+7]\displaystyle\int{\left(15\,x^2+2\right)\,\sqrt{5\,x^3+2\,x+7}} [math: dx] . Note: Type [math: c] for the integral constant. [math: f(x)=][input] Check Question 2

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