csc² In x dx. X

Q: (14) dx + xydy

A: Given

Q: 2x dx Using an appropriate substitution, evaluate:

A: It is a basic definite integration problem

Q: I. Evaluate /4x2 + 4x + 5 dx

A:

Q: Evaluate ∫1/(x^2-9)^3/2 dx using trignometric substitution.

A:

Q: 2.x? Evaluate dx using substitution technique. 2x' +5

A: Since Mulitple questions are asked, Hence doing only first question.

Q: Sx(2x – 3)®dx

A: Given, ∫x2x-38dx We have to evaluate the integral.

Q: Evaluate. d 2 dx

A: Use the power rule of the derivative, ddx(xn)=nxn-1 And, the linear rule of the derivative,…

Q: Find and simplify whenever possible. dx y =cosh3 2x – cosh 2x - 3

A: Given y=13cosh3(2x)-cosh2x We need to find the value of dydx dydx= ddx13cosh32x-cosh2x =…

Q: It is known that dx Compute . Simplify the final answer. 2х-у dx

A:

Q: dy - for y = 4x³sin¬lx. dx Determine

A: ddxsin-1x = 11-x2

Q: 3x dx 3,

A:

Q: 213 dx 4+x² ,2

A: We will use substitution to solve the integral

Q: 2 -J (x2/3 + 늪)dx

A:

Q: d -(In(5x + 4)) dx Find

A:

Q: ex dx 8. 1+ e2x

A: Given; I=∫ex1+e2xdx   ...1   As we know that; ∫11+x2dx=tan-1x+C

Q: 3 ex dx = e3 - e, use this result to evaluate Given that 5ex + 6 dx.

A:

Q: (е2х-1)2 dx е 2х

A: topic - indefinite integral

Q: Evalute, Se In (i+e) dx. 2. FuluO

A: As per our guidelines I am solving only one question please resubmit other questions   1. evalute…

Q: S(2 + vx)³ Vīdx

A:

Q: 3 2 (x+2) dx (x-1)3

A:

Q: Evaluate the integral.

A: Given: ∫01 tan-1x1+x2 dx To find: Value of the integral.

Q: evaluate ∫ (top of ∫ is 16, bottom is 9) (-x^(-1/2)+5) dx.

A: We need to evaluate ∫916(-x-12+5)dx

Q: S Væ(x + 4)dx

A:

Q: Evaluate: 0 xsinx 1 + x² dx

A:

Q: Evaluate √1 + x² dx dy ○ 2/3 ○ 2√2 3 O −1+2√2 3 O 1/3 8

A:

Q: Evaluate 3x? dx and , 3x² dx.

A: ∫02 3x2 dx=3x3302=x302=23-03=8-0=8

Q: Evaluate "x9/2 e-x/2 dx,[+hint: assume x = 2y]. %3D

A:

Q: 4 Vx en Cx) dx

A:

Q: – 4) 6x? – 4x 9x2 dx

A:

Q: 4 e dx

A:

Q: 2x + 3 dx

A:

Q: Use geometry to evaluate (x+1)dx. Draw a picture to illustrate the problem.

A:

Q: Evaluate A) Scos³x dx 4 B) Ssecx tanx dx

A:

Q: ese²x Evaluate Cotx 3. dx

A:

Q: Evaluate the follo 1) , 3x(x-5)dx

A: Given integral is: I=∫-123xx-5dx

Q: [2x/4 +x? dx

A: Here we have to integrate the given problem.

Q: 1 (a) dx, (22 – 8x + 15)i

A:

Q: Evaluate: 4e-2* dx. Show your work!

A: Please refer the attached image for complete solution.

Q: / Va? – 4 dx, х > 2

A:

Q: Evaluate a*|1 – 2x| dx.

A:

Q: 3. fesec'e Vran e* + 2 dx

A:

Q: dx Vsinxcos3x

A:

Q: -dx 8a2+5

A: We know that integration of (1/x) is( lnx + c) .     Here i attached the solution of this question.

Q: Evaluate. (Be sure to check by differentiatingl) 1 dx, x# - 3 9+ 3x

A: To evaluate: I=∫19+3xdx Use the rule: ∫1xdx=ln |x|+C

Q: (1) dx

A: L)

Q: Evaluate: ³²₁ [2³(x + y)³] dz dy dx

A:

Q: Sx(2x – 3)®dx

A: Solution

Q: 1 dx, x3 – 1 (b)

A: a3-b3=(a-b)(a2+ab+b2) first we will do then partial fraction then calculate the integration.

Q: Sx(2x – 3)®dx

A:

Q: Evaluate the integral.

A: We have the given integral as I=∫012x+3x+12dx On solving further, we get the result as…