g(x) = cos(x + T) + 2 %3D

Q: b. e4t cos x dx

A: Solution of the problem as follows

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: dy 3. dx y – x + cos - -

A:

Q: π/2 cos² x dx

A: This question can be solved using the concept of properties of definite integrals.

Q: X COS 4x dx;

A:

Q: Fimk ® y = e* Cos 2x

A:

Q: Calculate a) ∫x ln x dx. b) ∫cos (2x) dx c) ∫ 2x +1 dx        x² - 1 d) ∫20   (x − 1) 25dx

A:

Q: X COS(x) dx = k 0. x)UIs x (b) – 1.1365 (c) – 1.3651 (d) -

A:

Q: x3 e. ; V1-x4 dx f. J sin x cos x dx

A: e.

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

A:

Q: -2 e* sin(x) -dx 1+ x2

A: the solution is as follow we will solve the given problem by numerical method  Trapezoidal rule

Q: Find the general solution of cos x dy + (y sin x – 1) dx = 0

A:

Q: Find y' : In(cos² 3x) = e*+y + sin-1 y

A:

Q: (a) /4 1+3 cos² 1 d.x; COST dx3B

A:

Q: L(cos at) = s2 - a2

A: To verify that ℒcos at=ss2-a2.

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

A:

Q: , Sercoszx *cos2x dx 3.

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

Q: 3e" + 3x + 10 cos x + 2)dx .2

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: 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: (x*+2 cos x -1+ 20) = 205) = dx %3D fuse rules)

A:

Q: (4e²+7x°+5 cos z + 2)dx

A: Solve integration

Q: Solve the equation (y - (cos x)^2)dx + (cos x) dy = 0

A:

Q: 2:Solve: cos (x+ y) dy = dx %3D

A:

Q: Solve cos x(e2y - y) = e' sin 2x, dy dx

A: We have to solve the given differential equation.

Q: The antiderivative of Cos(3x)

A:

Q: O cos 4x + (Dx + E) C) cos 4x + (Dx+ Am Cm 2:

A:

Q: x cos x² 2. X C0 dx -siny

A:

Q: 3x e COs x dx

A: To evaluate:∫e3xcosxdx

Q: 3-4K dx 4xス - oK t coS T

A:

Q: d) x In y - 2 cos (4e") = 2 tan (x'y) e) --3x =0

A:

Q: y" – 3y' + 2y = cos(e-*)

A:

Q: 16 ) d du -1 cos и — 1<и<1 dx V1 – u² dx

A: As we know that the differentiation properties:- chain rule: ddx(f(g(x)))=f'(g(x))g'(x)…

Q: f Cos 6 x dx 2 Cos ²3x

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

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

A:

Q: 11.| V1- сos 2x dx COS

A:

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

A:

Q: 11. y= e4x %3D 2x 12. y= e cos 3x

A: We can solve this question using chain rule and product rule of derivative.

Q: y" + 9y = e" cos 3x + x² + x³e*

A:

Q: (b) Determine cos(x²) 2x dx by using substitution method.

A:

Q: 4x Cos x dx b.

A: Given :

Q: Find an equation such that y xe" cos(2x) is its solution.

A: To find an equation we derivative both side with respect to x.

Q: dy Solve cos x(e2y - y) - dx = e' sin 2x,

A:

Q: X cos (3x) dx,

A:

Q: 31. (a) |2x - 1| dx (b) 3π/4 1.T CT/2 \cos x dx

A:

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

A: Integration problem....