Integrate the following expressions: Sex-e (2x – e*). dx !! (x + cos2x). dx "/2 X cos2x.dx

Q: Find the indefinite integral: cos ( πx ) dx sin, ( π )

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Q: Evaluate the integral. /2 15 cos Jo s x dx

A: Given:          ∫0π215cos5x dx        =15∫0π2cos5x dx         =15∫0π2cos2x2cosx dx…

Q: S(sin5 2x) (cos 2x)dx

A: To solve this integral, a certain substitution is done. The substitution of sin2x=u is taken and…

Q: evaluate using Integration by Parts.

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Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Evaluate the following integral. [10 sin x cos °x dx 3 X COS X dx%3D

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Q: Evaluate ]e * cos (7x) dx. Seex cos (7x) dx = %3D

A: Explanation of the answer is as follows

Q: Evaluate cos √6x dx using a substitution followed by integration by parts.

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: Evaluate the following 1, intergral from 0 to π/2  of √(sinx -sin^3x) dx  2, intergral from 0 to 3…

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: Find the integration of the following   x2 / x sin x + cos x

A: Our Aim is to integrate the following expression given below:-x2x sin x+cos x -(i)

Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: Evaluate the definite integral. 1 cos (тx) dx

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Q: e" cos x dx

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Q: Evaluate the definite integral. 1. S(sin(2x) – cos(2x)) dx

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Q: So sin¹ (6x) cos (3x) dx

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Q: Evaluate the followingintegrals.∫x3√(2x+1)dx

A: Given integral is ∫x32x+1dx. Consider u=2x+1. Then du=12x+1dxdx=2x+1dudx=udu

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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Q: Find cosh a In(sinh r)dr.

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Q: Find  dv/dx,   v =  log(  n√( (1-cosx)/(1+cosx) ) ) Where n = 744.

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Q: 2. Find the following indefinite integral. et cos cos (3x)dx

A: To evaluate ∫excos(3x) dx

Q: SinX d x cosx +2

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Q: Use symmetry to evaluate the followingintegrals.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

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Q: Evaluate the following: dx 1- So n/3 4 sin x -dp- 1-4cosx 2- Jo x(Inx)

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Q: Rewrite using the order dy dz dx. [L² dz dy dx = 5 5. O dy dz dx

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Q: make the given substitutions to evaluate the indefiniteintegrals. ∫√x sin2 (x3/2 - 1) dx, u = x3/2 -…

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Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Evaluate the following integral: 1. sec^3x dx 2. sinx*ln|1+sinx|dx 3. (e^-x)cos2x dx

A: ∫sec3xdxApply integral reduction=sec2xsinx2+12·∫secxdx=sec2xsinx2+12lntanx+secxSimplifying,…

Q: . Estimate the root of the expression, f (x) = x² – cos x, using: d. MOSS using xo = -1 with error…

A: As per the question we have to find the root of the equation : f(x) = x2 - cos(x) = 0 With tolerance…

Q: Find cosh r In(sinh a)dr.

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Q: Evaluate the following integral 5sin^(-3/2) x cos^3 x  dx

A: simplify the powers and take out the constant from the integral.…

Q: Evaluate the following integral. |2 cos (2x)dx [2 cos (20)dx =

A: as per guidelines, I can answer only one question. To know rest, please re upload particular…

Q: Solve the following Exact DE using Method of Grouping. 3) () dx + () dy = 0 X-X y

A: Given:          2x-1ydx+x-x2y2dy=0     This is in the form of   Mx,ydx+Nx,ydy=0    where Mx,y=2x-1y…

Q: The integral x dx x² + √x² can be transformed to which of the following using trigonometric…

A: ∫xx2+x2-1-1dx=∫secθ.secθtanθsec2θ+sec2-1-1dθ=∫sec2θtanθsec2θ-1+sec2-1dθ=∫sec2θtanθtan2θ+tanθdθ=∫sec2…

Q: Evaluate the integral: square root of x cos(1+ x to the 3/2 power) dx

A: Evaluate the integral

Q: (x2 + 8x) cos(x) dx

A: We have to find the integral As per guideline we have to solve one question Please repost other…

Q: /3+ |æ| dx -3

A: Given integral, ∫-333+xdx

Q: Use symmetry to evaluate the followingintegrals.

A: Given: ∫-22x9 dx

Q: 2T COs x dx

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Q: Evaluate 1- x? dx 0. by Simpson's rale with n=5

A: Here fx=x1-x2 The interval is 0,1 and n=5. Hence the interval is divided into 5 equal parts.…

Q: find integral 2) S sin?xdx dx cos³x

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Q: Evaluate the following: 5x2 S dx V4-x3 a) S cos(x) cos(sin(x)) dx

A: a) ∫5x24-x3dx Substitute t=4-x3 and differentiate it w.r.t 'x' dtdx=ddx4-x3dtdx=-3x2dt-3=x2dx

Q: Evaluate the following 1, the intergral from 0 to 1 of (dx)/(√(7-6x-x^2) )

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Q: Evaluate the definite integral. 1. 2 cos-¹(x) √1-x² dx

A: Given Problem:- ∫-11-2cos-1x1-x2dx