Find the antiderivative of |5sin x In5 cos x dx · O 5cos x + C O 5sin x + C O 5sin x In 5 + C O 5sin x + C In 5

Q: Find the antiderivative of 5sin x In5 cos x dx 5coS x + C 5sin x In 5 + C O sin x + C In 5 5sin x +…

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Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: 3. Suppose that m and n are distinct (i.e., m n) positive inte- gers. Use the FTC to show that |…

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Q: Evaluate the integral. S 20x cos x dx Select one: O A.80 sin. 1 40x cos + C O B.20 sin n1)x+ 40x cos…

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Q: Find the following indefinite integral: int [u^3/(u+3)^2] du =  Did you remember C? hint * this…

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Q: Find the antiderivative of 5sinx In 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: What type of DE is the following? xydx + (x2 – 3y)dy=0 O Bernoulli in x Bernoulli in y O Linear in x…

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Q: 4. Evaluate the integral 2+ In? x -dx. x – x ln x (a) 3 ln |In a – 1| + 2(ln r – 1) + (In a – 1)2 +…

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Q: Evaluate the integral. Select the correct answer. 6 6 x In (19x) - 12/15 x + C none of these 16 x In…

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Q: Evaluate the iterated integral. 8 9 10 / // (x² + y² + z?) dx dy dz -8 0 0 8 9 10 /// ? +x² + z²…

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Q: Solve the problem. Integrate f(x, y) = sin(x2 + y2) over the region 0<x2 +y2< 100. O T(1 - cos 100)…

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Q: Evaluate the improper integral. 16 16 dy dx Vx + Vy 0 0 256 O A. 3 (1- In 2) 64 O B. (1- In 2) 128…

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Q: aps odrbes show that uyx = 1+ - and that var(Y|x) does not exist. on 1

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Q: and let ah -(-1'I Let In tan (a) for n = 0,1, 2 Intz 1) Show that In + Io+ り+! (-1)" for nal an-…

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Q: 13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3…

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Q: 2. Show that n n var ΣΧ) ΣΣον(Χ, X ). \i=1 i=1 j=1 Compare this formula with var(X+Y) = var X+var Y…

A: The equation is Var∑i=1nXi=∑i=1n∑j=1ncovXi, Xj.

Q: 1 Find an antiderivative of 9 x¹ +4 x6 ار داشته in the variable x where x > 0.

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Q: The Fourier cosine integral of J (x) D 0, 2, 0<x<3 is 0<x О а. 4sin(@)cos(@x) do O b. 8 sin(3@)…

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Q: Find the most general antiderivative. 4 9 dx 4 sin-1 x - In Ixl +C 4 sin-1 x + 9 In |x| +C 3.…

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Q: Evaluate the integral. Oin | +0 | C In (x-8)² x + 7 In |(x-8) ³² (x + 7) + Din ((x=83² ) +1 In C + 7…

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Q: Evaluate the integral. (Hint: u-sub) sec x tan x dx 5+ sec x O 5 In Isec xl + C O In 15 + sec xl + C…

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Q: Evaluate the iterated integral. 7 8 (x² + y² + z²) dx dy dz -6 0 0 7 8 (x² + y² + z² )dx dy dz =

A: Given that: ∫-66∫07∫08(x2+y2+z2)dxdydz

Q: Calculate the integral: /3 arctan(x) dr a) O 3x arctan x – In(1 + x²) + C b) O3 In | arccos x| + C…

A: we will apply the integration by parts rule: ∫(u·v) dx=u∫v dx−∫u'∫v dxdx And we also use…

Q: хах 11. The integral f 4-х2 is equal to 1 A. In | | + C C.-글m14- x리 + C 4 x+2 2+x B. In |4 – x2|+C…

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Q: Evaluate the integral S sin³ z cos² zdx O A. cos z 3 cos" z +c O B. cos z +c В. COS z + o C. cos z…

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Q: Eliminate the arbitrary constants 1. X = -Int, y= at + bt2 2. In y = C, sin ax + C, cos ax + 9x<-2…

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Q: Determine the indefinite integral. S()dx O x+c O 2/x +c O 3 3/x³ + c 2x² + c

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Q: To prove that 2 dx 1+ (In x)2 + In x+c = 2 In %3D X1 + (In x)2 we use the substitutions U = Inx then…

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Q: Evaluate the integral. csch (in x) coth (Inx) 7x A) 7 sech (In x) + c B) x csch (In x) + c © 2 csch…

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Q: 304² 3x Evaluate dx dy, by first Reversing the order of integrals. √36 + x3 Enter an integer or a…

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Q: 9. Let f(x) x In(10) Find the most general antiderivative. F(x)

A: Given data÷ So,we need to find F(x).

Q: Evaluate the integral. (Hint: u-sub) Cos x dx 1 + 4 sin x O! Inl1+4 nin x| + C 4 In |1+4 sin x | + c…

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Q: Use substitution to evaluate the integral. s1/5 sin(s/5 - 2)ds 1/5 6/5 sin(s - 2)ds = %3D

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Q: 2. Show that 8(x²-a²)= 8(cos - cos') = 3. Evaluate the following integrals, Is = h₁ = √dr 8 (2²-3x +…

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Q: 6. Show all work for how to compute: In(x)dx. (Show work for how to find the antiderivative 1 of In…

A: Use integration by parts

Q: 3. Find the integral * dx a² -2 x+1 a.-x - - x - In(x + 1) + C 2 b.x2 – x – In(x + 1) + C c.x2 – x +…

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Q: What is the integral of f sin² x cos² x dx? cos(z) sin³ (2) cos(z) sin(z) + 4 4 ○ sin(4z)+4z 32 +C…

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Q: entiation to find the derivativ 1 O A. In 5t +1 5T +1 (In 5t) OB. VE +1 Xc 5t In 5t + 1 2. 5tVi 1 In…

A: Answer: dydt=5ttt 12ln(t)+1

Q: Find the integral ſ cos³0 sin 0 d0 . Tentukan integral f cos³0 sin 0 de. 1 cos*0 + C 4 1. O 1 -coste…

A: Let's find.

Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

Q: 6. Which substitution can work to compute for the indefinite integral fx√√x + 5dx? A. u=x C. u=x+5…

A: we use substitution method to  find the value of integral

Q: 7. | (x² + + 2x) cos x dx

A: Apply the integration by parts in the given integral. Let  u=(x2+2x) ; dv=cosxdxThen,du=2x+2dx ;…

Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: In x + In(x – 1) = 10 In(x + 25) – In(x – 1) = 3 e2x – 2ex = 15 e2x – ex – 12 = Q %3D %3D -

A: i) ln x+ln(x-1)=10ii) ln(x+25)-ln(x-1)=3iii) e2x-2ex=15 Note:      Multiple part question are given,…

Q: (integral of -4 to 4) of 5*cos(3t)(delta(t))dt

A: Here,

Q: Evaluate the iterated integral. 6. 7 8 (x² + y² + z² ) dx dy dz -6 0 0 6 7 8 (x² + y² + z² )dx dy dz…

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Q: Evaluate the integral f cos z(1 - sin 1)-1/2 dr. O In (cos r) +C O In (sin z) + C 2-in(1- sin 1) + C…

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Q: Evaluate the integral dx x2 - 1 O In - 1|- In |r + 1| + C O In a- 1+ C O 2 In a+ 1|- In |r - 1|+ C O…

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Q: Let u = cos(4x) and du = e² da, then by using IBP, the integral [e²= cos(4x) e2x cos(4x) dx is equal…

A: Given, u=cos4x and dv=e2xdx. Formula for IBP: ∫udv=uv-∫vdu