Please determine Į In(x2 + 1) dx.

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: Evaluate the integral dx (3x + 15)²’ by making the appropriate substitution: u = dx + 15)?

A: To evaluate:∫dx3x+152

Q: Use Fubini's Theorem to evaluate .2 -dx dy. I + xy

A: Given :            ∫02∫01 x1+xy dxdy By Fubini's theorem, the above integral can be rewritten as ∫01…

Q: Use Green s theorem to evaluate the give (y² dx + 8xy? dy)

A: In this question we will use basic of calculus i.e concept of integration. We will use green's…

Q: Evaluate the integral dx (5ӕ + 10)2 by making the appropriate substitution: u = dx (5x + 10)? II

A:

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: To calculate the derivative of the given function using chain rule: y=3x2+7x10

Q: Find dy for all of : dx 1- y = x/Inx у

A:

Q: sp dy dx dz (1–z) Evaluate .

A:

Q: x In(x) dx, where x >0

A: Given query is to eveluate the integral.

Q: Evaluate I = | x(In z)² dx

A:

Q: Evaluate the integral. dx a > 0 (a² + x²j3/2?

A:

Q: d Prove In Jax| dx In x for any constant a. dx

A:

Q: Let -1 y = tan' 3x2 – 1 dy Then dx

A:

Q: Evaluate the integral VI- 1 /1 dy dx. – x² – y2

A:

Q: Evaluate the integral. dx 4 a > 0 (a² + x²)3/2?

A:

Q: dy Evaluate dx at point (4,2) given 3(x² + y²)² = 100(x² – y²).

A: Answer and explanation is given below

Q: Use this information to evaluate 1 (1- e)| dx %3D x=1 et - 1

A:

Q: g=ズ, a find dy dx %3D

A:

Q: . In (3xy) %3D х+ x5

A:

Q: Rewrite using the order dy dz dx. [L² dz dy dx = 5 5. O dy dz dx

A:

Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

A:

Q: Evaluate 2Sin x´dx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A: i)Given:        ∫242sinx2dx   Mid-point rule:       ∫abf(x)dx=∆xfx0+x12+fx1+x22+fx2+x32+...…

Q: e*dx e2x +1

A: We know that; ∫axdx=axlna+C And ddxcot-1x=-11+x2   Given: I=∫7cot-1exexdxe2x+1   ....1

Q: Use the substitution formula to evaluate the integral. Vx +1 dx B) 2/2 - 1 D) 3/2 - 3

A:

Q: 2e Evaluate the integral dx 2x +3

A:

Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

A:

Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: What is the I.F of dy/dx = y - xy^3e^(-2x)?

A:

Q: If y = V1-x² sinx, prove that (1–x²) +xy =1– x². dx

A: Given that :- y=1-x2sin-1x Prove that :- 1-x2dydx+xy=1-x2

Q: Evaluate the integral dx (2x + 6) by making the appropriate substitution: u = dx (2a + 6)°

A: To evaluate the given integral.

Q: Evaluate the implicit function by finding dy/dx of x³+3y=3xy

A:

Q: Find d when y = 3 In(In(In(x))) dy dx

A: Here we can find the derivative as below

Q: Find (x' In(x)). dx

A:

Q: 3 x2 Calculate the integral: dx V5 + a?

A: Given,          ∫3x25+x2dx

Q: Find de when y = In(1+ 5/æ) dx

A: The objective is to find derivative.

Q: Evaluate the integral: x² e3a dx

A: This question is related to Indefinite Integral, we will use Integration by parts formula to solve…

Q: 4-3x dy dx X,

A: its a multiple integral based question.so 1st we integrate with respect to y and then with respect…

Q: (a) Evaluate the integral [x (x* -1) ´dx by using substitution.

A: To evaluate the given integral ∫x3x4-12 dx by using substitution.

Q: Find the integral +C 1 dx x² – 16

A:

Q: a) Find the integral 3x7 dx dy . Vr – x2 -

A: Given, the integral is Here y = 0 and y = 1 and x = Öy and x = y2.

Q: Evaluate the integral. B 4х- 3 dx J2

A: To evaluate:

Q: (b) Evaluate the integral | xe * dx. (1- x)?

A: Given : The integral is ∫ xe-x (1-x)2 dx .

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: Find dy/dx for y = In(tan(2x²))

A:

Q: ग Use the Midpoint Rule to evaluate the integral fx sin(x)dx. D]2 co | Fo 프2 NN

A:

Q: 37. Use Fubini's Theorem to evaluate dx dy. 1 + xy

A:

Q: Find the integral [(x** +(-1)°x*!) In((a+2)x)dx b+1 с+1

A: The integral has been solved n attached in the second step.

Q: the integral (dx)/(xsqrt4x2+1)

A: