1) Evaluate each integral by substitution: (In x) dx a)f(x+1)(x +2x)'dx b)fxVx² +9dx 「ズ dx 7x+5 dx k)f - x/In x xdx of x +3 (x+6x + 1)dx d)4x- ldx (7x + 2) sin(In x), dx sec'(-) X dx m)f- Dfxe* dx x+1 of- Vx² +2x- 4 dx 2) Evaluate each integral by using inverse trigonometric functions: 1 V16-x o x+2

Q: Evaluate the integral of (3x2 + 9y2) dx dy if the interior limits has an upper limit of y and a…

A:

Q: Evaluate the integral. x sec (3x) dx + C

A: Topic = Integration

Q: Evaluate the indefinite integral; f Vtan 3x sec2 3x dx OA)-(2(tan [3x)^(3/2) ] /9 + C OB) I DON'T…

A:

Q: In V3 dx 1+e2cx

A:

Q: Evaluate the double integral of cos(x) with x from 0 to π/4 and y from 4y to π

A:

Q: Evaluate the integral or show that it is divergent.

A:

Q: Evaluate the integral. inegral (5x +1 )/(2x +1 ) (x-1 ) dx

A:

Q: sec²(x) √2-3tan (x) dx

A:

Q: Can we evaluate the integral of 1/(x^2+2x)^3/2 dx by using x= sec¿ - 1

A: Consider the equation

Q: Find the integral for the following : 3- Sdx dx 1 1- : 2- S e-*sec² (ne¯*)dx 2Vx+2x 1+ex

A:

Q: Evaluate the integral. dx x2 - 5x + 6

A: Given integral:

Q: Evaluate the integral. inegral  0 to 1 [(x 3 -4x -10 )/(x 2 -x-6 ) ]dx

A: Consider the following definite integral:…

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: Evaluate the integrals in ∫sec x dx/√{2ln (sec x + tan x)}

A: Given  The integration is I=∫sec x 2ln(sec x+tan x)dx

Q: Evaluate the integral / f(x) dx, where -1 -{ if – 1 < x < 0 if 0 < x < 1 -X - f(x) = 1-VT - x²

A:

Q: 33. Use integration by parts to find the indefinite integral. fxcos(2x)dx -xcos(2x)–sin(2x)+c а. b.…

A: To find the integration

Q: (b) Evaluate 1 (x-2)¹/3 dx by using properties of improper integrals.

A: b Given integral is ∫131x−213dx. We have to evaluate the given integral by using properties of…

Q: Evaluate the integrals below: 1 2y .dx cos3x а) .dx, b) 0. lelsin3x – 1)

A: Here I am attaching image so that you understand each and every step.

Q: 4 dx = x² + 1

A: Given that, ∫-114x2+1dx=4[tan-1x]-11 =4[tan-11-tan-1-1]=4[π4-(-π4)]=4[π4+π4]=4×π2=2π

Q: x cos x-sin x Jr dx x²

A:

Q: Evaluate the integral

A: Given: I=∫xdxx2-7 for evaluating given integral, in given integral we substitute x2-7=t…

Q: Evaluate the integral dx ,2 2x x - 3x X

A:

Q: Calculate the integral ∫dx / √(x2−8)3.

A:

Q: Evaluate the integral of 2x/(2x^2 + 4) dx if the upper limit is 6 and the lower limit is 3.

A:

Q: Evaluate the integral 4х + 5 dx. 3 - x2

A: To find the integral

Q: Calculate the approximate to the integral -5 (24 +2x² − 3)dx, by the composite midpoint rule with…

A:

Q: Evaluate the integral. 3 dx -2

A:

Q: Evaluate the integral. x sec2 (3x) dx = +C

A:

Q: Evaluate the integral. sec x tanx dx 2 + sec x -In |2 + sec x| + C O In 12 + sec x| + C 2 In Isec x|…

A:

Q: 9. Write as a single integral in the form f(x) dx. -1 f(x) dx + f(x) dx - f(x) dx -4 f(x) dx

A:

Q: 1 dx 1+ Vx 3

A:

Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

A:

Q: 2. Use reduction formula to evaluate the integral: fsins x dx.

A: Reduction formula

Q: 6x dx (x³+1)*

A:

Q: Evaluate the integral: f/2 sin(4t-u) du dt

A: To evaluate: ∫π2π∫0tsin(4t-u) du dt

Q: Find the integral [(3x² – x) In(3x)dx .

A: Given query is to solve the integral.

Q: If the substitution x = sin y is made in the integrand of . - A dx, the resulting 1-x integral is

A: Put value in  given  integral

Q: Find the product of the integral 1- L sin(x)ecos(x)-2y dxdy

A:

Q: evaluate the defmite Integral га (X -2)dx 4.

A: Given integral:

Q: 20. Verify by differentiation that finx dx = x(In x-1) + C, then use appropriate changes of…

A:

Q: or show that it is divergent Evaluate the integral dx 10

A:

Q: Evaluate the integral. . 4 1) x In 2x dx 1

A:

Q: Evaluate the integrals in 1 1. Vx(1 + x) sin x sec x dx

A:

Q: + 3x dz. x2 + 1

A:

Q: Evaluate the iterated double integral JI-X² ( [√x² sin (x² + y²) dz dy dx

A: A a couple of imperative is a specific imperative of a characteristic of numerous actual variables…

Q: Evaluate the integral. 7 - x2 | x5y dy

A:

Q: 4) Reverse the order of integration in 2 2x x' dydx 0 x2 and evaluate the integral as an x-simple…

A: To reverse the order of the below integration. ∫02∫x22xx3dydx

Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y

Q: find | (In(x)dx 2 3 Improper Integral

A:

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

A: