Show that (In kx) dx (In x), where x > 0 and k is a positive dx real number.

Q: Find the indefinite integral.

A: To Find the indefinite integral. Substitution  u = x3 du = 3x2 dx du/3 = x2 dx

Q: q dx (6x²+ 32) dz

A:

Q: |x-4|dx

A:

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: 1 |x+1|dx -2

A: ∫-21x+1dx

Q: Evaluate iterated integral.

A: We have  I=∫34∫126x5+yx dx dy   Integrate with respect to x. We get I=∫346x25×2+ylnx12…

Q: Use geometry to evaluate the definite integral -2∫2 √4−x2 dx

A:

Q: Evaluate the integral. бх + 2 dx = | x2 + 2x – 3 -

A:

Q: Evaluate the integral. 1 -dx (x + 8)(x² + 9)

A:

Q: use a geometry formula to find the exact value of the definite integral  lxl dx on the interval…

A: Line AOC represents the graph of y=mod x in interval [-2,1]. Here coordinates of 0 are (0,0), A are…

Q: Consider the indefinite integral 26 dx: (x7 + 6)"

A:

Q: Evaluate the integral. 4 x - 3 dx X 1

A: Given:

Q: Use substitution to find the indefinite integral

A: Given, ∫2+lnxx dx

Q: Use substitution to find the indefinite integral.

A: Integration by substitution is a method to solve integrals line in the above question where the…

Q: Consider the indefinite integral 4 dx

A: Given,           ∫44+exdx

Q: Evaluate the integral. 3 x - 3 dx 11 X

A:

Q: 2 dx x3 - x

A: We will find the integral as following.

Q: Evaluate the double integral : 8. dy dx 88 -

A: We have to evaluate the given double integral   The given expression is

Q: +oo So xe-dx = 1

A: Evaluate: ∫0∞xe-xdx Apply infinte integral property: ∫a∞fx dx=limx→∞∫axfx dx ∫a∞xe-xdx…

Q: xe dx

A:

Q: Use substitution to find the indefinite integral

A:

Q: Evaluate the integral. S-x cos(3x) dx

A: Use integration by parts method

Q: find integral 1/ sqrt ( x2 - a2 ) dx , where a >0

A:

Q: Evaluate the definite integral.

A: ∫15x2x-1 dx Consider, ∫x2x-1 dx Put, 2x-1=t⇒21-0=dtdx⇒2 dx=dt⇒dx=dt2 Therefore, ∫x2x-1 dx=∫t+12tdt2…

Q: /1 x² dx /2 2 x2

A: I am going to calculate this integral using trigonometric substitution.

Q: Evaluate the integral. ▪4 x – 3 dx /1

A:

Q: Evaluate : Integral from 0 to 2 : 2x^2 e^-2x dx

A: To determin the value of the definite integral.

Q: 6. |dx x

A:

Q: (x-1)* dx

A:

Q: Show /x^ In х dx xn+1 ((п + 1)In x — 1) (п+1)2

A:

Q: Use substitution to find the indefinite integral. 4x° e 4x* dx .3 e 4x* dx =

A:

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: Use U-Substitution to evaluate the indefinite integral. S(5x + 2)?dx S 2x sin(x²) dx

A:

Q: The integral csc(0.5) dx is equal to

A:

Q: Evaluate the integral: 1 2x + 4 dx x² +1/

A:

Q: Evaluate 0, dx by dividing the interval into 10 equal parts 8х-5 by using Simpson's one - third…

A:

Q: (E) dx 4 2. \(3x-5)2,

A: We have to evaluate the given definite integral.

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: find the indefinite integral 1十xe dx

A: To find the indefinite integral  integration (6/(1+x²))dx

Q: Consider the indefinite integral dx: + 8)°

A: Given,  ∫ x5x6+86dx

Q: Evaluate the integral. x² + 25 dx of

A:

Q: evaluate  integral 0 to 3  1/ x-1  dx if possible.

A:

Q: Find the integral 1 dx = 9 – x²

A: We have to find the integral: ∫0119-x2dx Simplifying the question so that we can use the table of…

Q: Evaluate the definite integral. 1 dx V2-x

A:

Q: Use property 8 to estimate the value of the integral 1,12 15/0 - 58 a dx.

A:

Q: dy Find in terms of x and y if x In y + yo = 4 ln x. dx

A: Solution is written in below steps.

Q: use a geometry formula to find the exact value of the definite integral (-2x+4) dx on the interval…

A: We have to find the exact value of the definite integral (-2x+4) dx on the interval [3/2,1/2]As a…

Q: 0. (7x + 10e") dx 1.

A:

Q: Evaluate the integral. „ 3X + 7 e ~×) dx , 3× + 7 e ~×) dx =

A: