S sin(4 + 5x) cos (5x – 4)dx

Q: 4. | e2x cos 3x dx

A: NOTE: You have posted multiple questions, we have solved the first question for you, if there is a…

Q: 1. e2x cos 3x dx

A: ∫e2xcos3xdx

Q: 6. dx dy + cos.

A: Given: dydx=yx+cosy-xx

Q: x sin wx O Show that dx = x² + 6x + 10 (3 sin 3w + cos 3w) w> 0

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Q: dx (2) 3y sin x 2xy cos x = 0 dy (3) 3x²y² + 2x³y -= 0

A:

Q: 5 dx Find dx, x> V25x? -9 5x In 25x2-9 + C 3. sin-13x+c 1+9x2 +3x|+c 1 V1+9x? + C 3x 3. + C V25x2 -9…

A: The solution is given below in the next step:

Q: d [ sin(x)cos(x) dx dx 1+x4

A: Find the integral

Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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Q: (16) cos (xy) find dy/dx

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Q: cos 2x 12) S 2cos2x sin x – sin x dx -

A: To integrate:∫cos2x2cos2xsinx-sinxdx Solution: ∫cos2x2cos2xsinx-sinxdx On simplifying further we…

Q: 3r cos(x) 1. Evaluate dx V1+ sin(x)

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Q: S+ xcos (nx) dx + (π-x)(cos(nx)) dx

A: Here we will use integration by parts  let f(x) and g(x) are two function of x then…

Q: |3 cos(2x – t/ 2) cos(x+ t/ 4)dx

A: To evaluate the integral: ∫3cos2x-π2cosx+π4dx Solution: We know that, cosa cosb=12cosa+b+cosa-b…

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: S" sin" (0.5x)cos (0.5x)dx

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Q: (d) ƒ sin(1 – x)(2 – cos(1 – x))ª dx

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Q: 4 sin x dx (1 + cos x)²

A: Here we have to solve the given integration.

Q: 3e"dx 3x 1. 3x – 16 2. x 10 – 3x°dx 3. / In (cos®) an@ de 3.

A:

Q: COSX sin x dx 4. S 1-ఆశి అరికి న

A:

Q: 3. ſ cos(3x – 2n) cos (x + 1) dx

A:

Q: dx (2) 3y sin x - -2xy cos x = 0 dy

A: Follow the procedure given below.

Q: (a) / sin sin(8x) + cos(7.x) dx (b) / (3x – 5 sin dx 2 (c) / cos(3t) + sin(5t) dt

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Q: 2x cos x? dx 1+ sin² x² 8

A:

Q: 1. § e sin 4x cos 4x dx 2.5 dx Se-2x dx %3D

A: 1) Given:                ∫esin 4x cos 4x dx Apply u-substitution: u=sin 4x⇒du=4 cos 4x dx…

Q: Take the derivative of this integral.

A: Given

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: S cos(3x – 2n) cos (x + t) dx

A: We know that, 2cosAcosB=cos(A+B)+cos(A-B) Also, ∫cosxdx=sinx

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

Q: y = sin(3x) + cos(0.5x)

A: Given: y=sin(3*x)+cos(0.5*x) We have to determine the value of y,where x varies from 0 to 2pi in an…

Q: find dy/dx. y = x2 cos x - 2x sin x - 2 cos x

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Q: 7T, 0 cos( {*) cos(2y)dx 2gin( gx) sin (2) dy 77

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Q: 4 sin' 2x cos 4x dx 4.

A:

Q: -3π/2 2. S TL √sinx + 1 cos x dx

A: We solve the given definite integral by using substitution method .

Q: [2xy cos(x²) – 2xy + 1]dx + [sin(x²) – x²]dy = 0

A: The solution attached :

Q: find dx 20. 19. 0 do 21. 22. dy -2x sin 2x dx cos 3x dx 23. 24.

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Q: dx = 3 cos° x/2sinx

A:

Q: f Cos 6 x dx 2 Cos ²3x

A: Solving the problem by finding the value of the problem.

Q: S sin x (1+ cos 2x)² dx

A: In some cases integrals can be converted to standard integrals using an appropriate substitution.…

Q: 1 S (4x4 – e3* + cos(2x) – + 5* ) dx - x-1

A: First you need to go through the formula of calculus. Specially go through the details of the…

Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

A:

Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: 5 cos(a) sin (x) dx

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: 3. Find dy dx y= 3 Sin.

A: Find derivative

Q: d²s dt2 sin 3t + cos 3t |

A: In this question, we need to find s.

Q: dx b) sin 2x sin x dx (3x + 2)²

A: we have to integrate

Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

A:

Q: x2 sin3(x) Q.2\ Find dx if y = In cos(x*).V1+x/

A:

Q: dx 3+2 cos x

A: The value of the given integral is 2√5/5 Arctan[√5/5 tan(1/2 x)] + c

Q: 7. Find (a) y = (x* + 5x) cos 5x %3D dx

A: We can find the derivative using product rule as below

Q: (3e + 10 cos(x)) dx ntegral =

A: Integration problem....