Use residues to derive the integration formulas in Exercises 1 through 6. dx TT 1. 0 x²+1 2 dx πT 2. (x² + 1)² 4°

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

A: Integral by parts

Q: 3.) Integrate using an appropriate technique: 24100 dx (show all steps) 4x2 + 24x+100

A: We have to evaluate

Q: 2 6. dx (sin x – cos x)?

A:

Q: dz. 2ª + 9 tegrate

A: The integration of the integral x/√(x4+9).

Q: 2 (In x)² x3 da

A: Introduction: The definite integral of any function can be expressed either as the limit of a sum…

Q: 7 I √49-x² 49-x²-z² Ľ -V 49-x² 1 √49−x²−z² (x² + y² + z²)¹/2 dy dz dx =

A:

Q: dx V (1+ Vx)

A: Since you have asked multiple questions, according to our company guidelines we are supposed to…

Q: sinh In(2+2x) dx? x+1

A:

Q: S sec x dx Use Integration by parts to solve

A:

Q: -cosh(2x² + 1). Evaluate (A) 4xsinh(2x² + 1) B 2xsinh(2x²+1) C) xsinh(2x2 +1) с D (2x2 + 1)sinh(2x +…

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Q: tan-x is dx using integration by parts Find x2

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Q: (16-9x)7 dx

A:

Q: 2 x² +1 -dr. VI Calculate

A: ∫xn=xn+1n+1

Q: Find the values of d/dx (11) and d/dx(π)

A: Consider the provided information, ddx11   and   ddxπ. Find the values of the derivative. The…

Q: I [20 / (e(8-10x) dx. The integrand equals 20 divided by [e raised to power of (8 - 10x)]. O…

A: ∫ex dx =ex+C

Q: Solve (cosx)dy = (sinx)dx

A: The objective is to solve the expression cosxdy=sinxdx

Q: Find O d² cot 1 ¹x dx2 -2x (1+x²)² 2x (1+x²)² -1 (1+x²)² -2 (1+x²)²

A:

Q: d^2y/dx^2 + 3dy/dx + 4y = 3x + 2 Utilize the indeterminate coefficient technique to solve the above…

A: Here is the, solution

Q: 3 A = (18х — 6x?) dx 6x2) dx *3 = 6 (3х — х2) dx = 6 3. II II

A: