Using the substitution u = x³ – 1, ƒ±₁ x² (x³ — 1)5 dx is equal to which of the following? O O 63 -2 f₁u³ dy u du Of u³ du 03 fuº du

Q: II Evaluate the following by simple substitution: (x+5x²+4xY X-1 2. S sin24xcos4xdx

A: 1.∫x3+5x2+4xx-1dx Let x-1=t ⇒dtdx=1⇒dx=dt So, x=t+1 Now x3+5x2+4xx-1=(t+1)3+5(t+1)2+4(t+1)t…

Q: How many positive real roots are there in the equation 7x+5x+3x³+x=0? a. 2 b. 0 c. 3 d. 1

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: If 3y - 2x = 10, then " at (-1,2) is dx O a. 4 3 O b. -2 3 O c. -4 3 Od. 3

A: Find the derivative of the equation at a point

Q: | (2æ – 9)sin (a? 8) dæ = Evaluate 9ж + - Include all steps in your written work.

A: The given integral,∫052x-9sinx2-9x+8 dx

Q: Let a be a constant. Evaluate + x? + a) sin(9x³) + 9x²)dx.

A: Given integration is ∫-22(x4+x2+asin(9x3)+9x2)dx     Which can be re-written as…

Q: Integrate the following. 3. f sec?x dx tanx

A:

Q: Q3. Evaluate ". -2n sin²0 de 5+4cos0

A: To Determine :-  ∫02π sin2 θ5 + 4 cos θ dθ

Q: 2TT Sin nx dx

A:

Q: x dx in two ways: using the direct substitution u = x² – 4 x? - 4 and by trigonometric 11. Evaluate…

A:

Q: d 50. (8u3/4 + 4и 1/4) du

A:

Q: d99 Find (sin x). dx

A: Consider y = sinx. Compute the derivatives of the above equation.…

Q: dy If = cos 2x, then what is y? dx

A: We will solve the problem

Q: dx 4. Evaluate cos? ' x (tan x + 1)

A:

Q: Solve the ODE. dy dx (ye²y - sin x - x²e³). = y cos x + 2xe" - sec² x

A: Given

Q: it メ=う,TLXム2 3TT find: a: sinkx),

A: since you have asked multiple questions in single request so we will be answering only first…