S (12a³ + 6) arctan(x) de;

Q: a- S 3ln²x_dx b- f sin5x.cos²x.dx

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Q: sin x dx 4 3 Show that -

A: The integration can be written as;

Q: Q3- Find i) S sin3x.cos(-5x)dx

A: We have to evaluate the following integral: int sin 3x . cos (-5x) dx

Q: x³Væ² + 1 dx

A: Solve the integration

Q: 3) S x tari'x dx X,

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Q: 2x + 2 Evaluate : sin :Ssi". dx. 4x² + 8x + 13,

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Q: (A) ftan (5x)dx dx √9-4x² (C) [sin 6x cos7x dx

A: According to new guidelines if a question contains more than 3 subparts we have to solve only 3…

Q: y = e2* sin 2x + e3* cos 2x

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Q: b) Z = Arctan ( x² /y³)

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Q: fcos cos² xdx 2.

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Q: y = sin(3 – 4x)" %3D

A: Apply the chain rule of derivatives, If y = f(g(x)), thendydx=d(f(g(x))d(g(x))×d(g(x))dx

Q: |( + 3t) sin(2t) dt 13.

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Q: fo (9 cos(x) – 2 sec²(x)) dx

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Q: V sin2(x32 - 1) dx, with u x32 - 1

A: Consider the integral ∫(√x)sin2 (x3/2 - 1) dx.

Q: Find the General and Particular solution of = -8 sin 4x ; y = 6 when x = o dx

A: As there are multiple questions, first one is solved here.

Q: x fare cos = dx 2

A: Indefinite Integration

Q: -2 Ssin®(3x)cos(3x) 5 dx

A: Given, ∫sin53xcos3x-25dx We have to find the integration.

Q: S(6Vx + 3 cos x - 8)dx

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Q: Solve the D. E J+gtanx = sin ex

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Q: 1 x³ y =e*(dsin²3x-tanx ) - 10 y'=? (fх +1)

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Q: S cos^3 (x/3) dx

A: ∫ cos3(x/3) dx ∫ cos(x/3) cos2(x/3) dx  ∫ cos(x/3) (1-sin2(x/3)) dx.         ..(1) (Beacuse…

Q: 4In(Arctan x) = 1-y

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Q: , Sercoszx *cos2x dx 3.

A: Since multiple questions are asked answering the first question, repost other question for solutions

Q: 1. Use a substitution to find (6a2 + 2)e*+# dx showing working.

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Q: fxcos (x)dx COS

A: Assume u=x^2Find du

Q: 2. y = ₁³x cos x + c₂e³ 3x Ge 3x sinx

A: Find out the differential equation by elimination of arbitrary constants.

Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: 2. xy' -y == y cos 3x

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Q: 13. (D² -1)y = x³ sin 3x

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Q: -r°(1-cos2x) 1- dx 2

A: 1). To evaluate the integral: ∫π01-cos2x2dx Solution: Evaluating the given integral.…

Q: S dx = sin-1+c 9. V6x-x2 3

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Q: Find d2y/dx2 implicitly in terms of x and y 7xy + sin x = 2

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Q: S2(cosx)(sin2x)dx %3D 3.

A: .................(1) take  put all values in equation 1

Q: 4-x2 C. ye arccos

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Q: 1. D² {Sin ² x 3 2. JD²-15² √2e²x3

A: Here D is the differential operator. D=d/dx

Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

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Q: 1 x³ -1 y =e*(dsin 3x- tanx')+- 10 y' = ? (fx +1)

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Q: 2. Sin 2x dp X UIS 6.

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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: solve the nonhomogenous equation y''' - 6y' = -cos(x)

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Q: y = Arctan 2+x 1-2x

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Q: a) f(x) = 10r23 + el2 + 53 - In(r)+ arccos(x) %3D

A: Given

Q: a²-x2 6- Sº, S dy dx -Va2-x2 7- Sx? cos 5 x dx

A: As per bartelby guidelines we have permitted answer only one question if given more than one…

Q: Q1-Find S sin 3x e4* dx

A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx…

Q: Find 1-x if y = cos-l dx 1+x²

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Q: e-3t sin (4t) y (0) ==

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Q: c) Se- sin(4t) dt

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Q: Solve f 8x cos(7x) dx using Integration by Parts.

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Q: 3x dx | sec 2

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