2. 1- x2dx cos(x + 1) dx 3.

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: 1. Given y= [In(3x² +8)] dy find tan(6x) dx

A:

Q: dy 3. dx y – x + cos - -

A:

Q: 6. dx dy + cos.

A: Given: dydx=yx+cosy-xx

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

A:

Q: 8. y" +4y' = e* cos 2x

A:

Q: 7 6.) Let Y 4(cos' (3x+3)> ニ Find dy dx

A: The given function is y=4cos73x+3. Obtain the derivative as follows.

Q: J cos 3x cos 4x dx :

A:

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: 1. Determine the general solution of this equation in terms of C ( sin y- ysin x) dx + (cos x + x…

A: We have the following solution for given ODE:

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

A:

Q: 11. sin(4x) dx e 0.

A: Given: To evaluate:   The given integral.

Q: Can you help me step by step?

A: According to the given information the given function is:

Q: dy/dx= 4 cos 4x

A:

Q: If y = cos 3X find dy/dx: y = cos?3x = (cos 3x?. (cos 3x )?. %3D

A: Given, y=cos23x=cos3x2

Q: •1/2 | cos(T(x + 1)) dx -2

A: First remove the upper limit and Lower limit and then substitute to make the problem simpler to…

Q: 4) Find when y? - x2 + cos(x + y) = 0 %3D dx

A:

Q: x fare cos = dx 2

A: Indefinite Integration

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

A:

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

A: Follow the procedure given below.

Q: 211 211 S cosr nx dx= | [cos nx cos nx dx = 0. %3D

A: The detailed solution is as follows below:

Q: 4. ſ cos xesinx dx

A:

Q: 1 E valuate [ (x' + cos(3x)) dx sin (3x) a) b)

A:

Q: 3) f₁ dx do - cos 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: 3) S cos(Inx) dx

A: according to guidelines we should able to do only one question at a time #3

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: b) S. cos x cos 7x dx

A:

Q: | 1. Find dx dy for the following functions : 45) y=x' log,(3– 2x) (ans.:3x² log,( 3 –2x)-73-2x…

A: We have to find the following derivatives

Q: 1. Given [In(4x² +7)ľ° y= find dx dy tan(5x)

A:

Q: S S som'e dx cos'x

A: Perform integration

Q: 3+6 b. (2xy-sin x) dx + (x-Cos yldy

A: Topic:- solution of differential equations

Q: 3x e COs x dx

A: To evaluate:∫e3xcosxdx

Q: 5 Find *: (a) y = cos(11x + 2x) dy

A:

Q: 2. 2メ dy dx for y = Cos (ln x + e put lに

A: y = cos2(ln(x) + e2x)

Q: 1. x2 cos 2x dx

A: The given integral is: ∫x2cos 2x dx

Q: 9. ſ csc 3x dx 10. S sin x e cosxdx CoSx

A:

Q: 11.| V1- сos 2x dx COS

A:

Q: 1. " x² cos 2x dx

A: (1) We need to evaluate the following integral ∫0πx2cos2xdx

Q: 3. Find (in simplest form) dy/dx: y=In(4x² – 3) cos.x b. y=e0s* а.

A: We have to find dydx: a.  y=ln4x2-3b.  y=ecos x We know the formula of derivatives, dxndx=nxn-1d…

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

A: Find derivative

Q: 211 211 ( cos nx dx= | [cos nx cos nx dx 0.

A: given that                               ∫02πcos2nxdx=∫02πcosnx cosnx dx=0 now,…

Q: E valuate dx 7-3 Sin X +6 Cos X

A: solution.

Q: 4x Cos x dx b.

A: Given :

Q: 7/2 d sin dx dx COS

A:

Q: dy = 4 cos 4x dx

A: The given differential equation is dydx=4cos4x. We can solve this differential equation using…

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