5. Solve the following indefinite integrals. a) f(x¹.3 +7x-2.5 + ln(ex"))dx

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A: Solved below

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A: Given query is to find the integral.

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A: To evaluate the integral.

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A: We can solve this as follows:

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A: First we need to simplify the given trigonometric ratio and then integrate it accordingly.

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A: Given; (2x3-1)/[(x-1)(x+2)(x2+1)2].

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A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

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Q: 18) Determine the annihilator of y-z-efsinz. a) (D-2D³-2D²)y=0 b) (D+2D³ +2D²)y=0 e) (D¹+2D³-2D)v-0…

A: The given equation is; y=x-exsinx.

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A: use separtion of variable and integral

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A: use the algebraic property of integrals.

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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A: Let's solve given differential equation.

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A: note ; -  since you have asked multiple questions but according to bartleby i only have to solve…

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A: we will find the required.

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Q: Find the exact length of the curve. x = 8 + 12t2,    y = 3 + 8t3,    0 ≤ t ≤ 2

A: Given that:   x = 8+12t2 and  y = 3+8t3 , 0&lt;=t&lt;=2. Find the exact length of the curve.   Here…