Use integration by parts to find the following: f(t Hint: Use the substitution (t + 7)e²t+³ dt = = +C u=t+7 and du: e²t+³dt =

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A: We have given;

Q: CALCULATE (16t³, –9t², 25tª) dt.

A: To evaluate the given integral- ∫01(16t3,-9t2,25t4)dt Here we will use the following integration…

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A:

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A:

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A: Given, y=sec-1x

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A:

Q: Given y = x³ 11 Bac 2³/27x² + 2x, find dy dx H Use the math type b

A:

Q: y = (r² + 4r) e"

A: given question is solved with the help of product rule of differentiation    i.e. (f.g)' = f*g'+…

Q: 9t2 dz dt +61 - 2 = 0. A Check Answer

A: The given differential equation is Lets solve it using integrating fractor.

Q: Find the Integrating factor of: dy + y. sec5x = tan5x dx 1 (sec5x + tan5x) 5 O sec5х — tanп5x + 5 O…

A:

Q: dxdy Vy X'

A: Given: ∫01∫yy21y2-x2dxdy

Q: -t,x-1 dt

A: Please see the explanation below

Q: Rearrange the equation to isolate (a + b) (d_e) = f a

A: (a+bc)(d-e)=f(ac+bc)(d-e)=f

Q: Find dy 3 2. -3x

A: Given that, f(x)=x3-3x We have to find derivative of the given function.

Q: x?dx V1-x6

A: 1). To evaluate the integral: ∫x2 dx1-x6 Solution: Let substitute t=x3. dtdx=3x2dt3=x2  Substituting…

Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 500 + 900t - 90t², where t is…

A: Given that the traffic flow rate is    rt = 500 + 900 t - 90 t2      The time taken 6 A.M. as t = 0,…

Q: Solve the equation in the attached image:

A: Given:

Q: Q3. Integrate: ] x+4X*+4X

A: we have to solve :∫x+1x3+4x2+4xdx

Q: Calculate for w = xyz. By

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Q: INTEGRATE dx ¹.Sa 4x1 2.fdx

A: According to question,Given Integral,1. ∫dx4x-1

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A:

Q: For F = xy+xy+1 0, calculate: dy_ dx ây

A: Given,          F=x2y+xy+1=0