1. Integrate: [x³ sin(2x) dx.

Q: So Jo (sin x + (sin x +4)² dx 0

A:

Q: d sin Vx dx II

A: to find the derivative proceed as follows  ddxsinx=cosxddxx

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: d) sin (x)e3*+ dx dx

A: The given integral is definite integral because limits are given.  So integration value will be a…

Q: /4 tan x dx /4

A:

Q: d [sin? (In x)] dx

A:

Q: dx (x² +25)3/2

A: To find the integration.

Q: |5sin(4x + 5) sin(2x --) dx

A: We need to evaluate the given integral. We will use the formula  Cos(A+B)-Cos(A-B)=-2 SinA SinB

Q: a dx =? (1+sin x)sin x

A:

Q: d cosh(3x? + 1) and (b) dx d (sinh x tanh x). dx Calculate (a)

A: Given: a ddxcosh3x2+1b ddxsinhx tanhx

Q: Find [(x- sin(2x)) dx

A:

Q: sin 5 (17x) dx = [

A: To evaluate : ∫sin517xdx Let I = ∫sin517xdx ⇒I =∫sin417xsin(17x) dx

Q: (e) sin(2x) sin(x) dx.

A: ∫sin2xsinxdx

Q: Integrate (sin1/2)(x)dx

A: The given integral is ,∫sin12x dx=∫sinx2  dx

Q: 4 cot (8x) C&x) csc^C8x) dx

A: solve integeration

Q: y = | cosx + x² dx

A: Use the basic concept of integration and solve the indefinite integral.

Q: ソ=xX.sinx

A:

Q: dy Find dx y = tan (In 6x) dy dx

A:

Q: sin(In()) dar.

A: We use integration by parts to find the value of the given integral. If f(x), and g(x)  are two real…

Q: y= sin (0.25) + sinh (2).

A: According to the question, we need to evaluate the function: y = sin-1(0.25) + sinh(2)

Q: 3.a) Find dx y = ln(2x - 4√x). b) Find dx y = ln(In(sinx))

A:

Q: 1. Determine (i) |cos (2x– 7) dx dx (ii) x +9 (ii) dx 4-9x² 2. Determine (sin x cos x dx using (1)…

A: Since, you have posted multiple questions we will only first question with three subparts as per our…

Q: ∫sin5(6x)cos(6x)dx

A: ∫xn=xn+1n+1+C

Q: a) Integrate the following functions i. (-2x² – 9x – 7)dx (4x* – 9)* (20x“ )dx. [-4e"dx ii. iii.

A:

Q: Find the value of

A: To find the value of ddxtanxx=π3.

Q: d. f(x)= sin (1-x)

A:

Q: sin x = x (1 + tan y). Find and provide solution for dx/dy

A:

Q: Evaluate : e2x sin3x dx

A: Introduction :

Q: e2x sin(5x) dx

A: Given,  ∫e2x sin(5x) dx

Q: tan?(x) sec(x)dx trig property 2. 2)

A: We have to solve the integral