x 3 X 14.J. J16-x 2 -dx V16-x² dx 15. Vx -1 4

Q: •2 1 -dx- J-3 (x + 7)(x² + 16)

A: Given integral is Apply partial fractions to break the denominator

Q: 8 3x -dx 3 3 V 2 – x 2 -

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Q: H-w 2x +3 dx メ+2 X X 3 X2+ 2X+1

A: Topic:- application of integration

Q: 2dx J x (3(ln x)2 + 12 ln a – 15) -

A: Answer

Q: 14.1 dx V16-x dx 15. . Vx -1

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Q: 3x +2 J. - dx. (x² +9)(x– 4)x 10. Find the principal value of

A:

Q: .2 x+3 Evaluate / -dx (x+1)(x²+1)

A: Given integral, ∫x2+3x+1x2+1dx

Q: 1. у%3D х3 — 2x2 + 3х — 5 y = 3 — 2х2 + 3х — 5 dy — Зx2 — 4х + 3 dx

A: Given: y=x3-2x2+3x-5

Q: intergral 1/20 1/((x-1/2)2 + 3/4) dx

A: Formula Used: ∫1x2+1dx=tan-1 (u)tan-(0)=0tan-1-13=-π6

Q: 14. (x + 3x – 1) dx 15. dx tU +1) -G² – 1)]dy 16.

A:

Q: intergral x^e^3x^2+1 dx

A: I=∫xe3x2+1dx Then let I1=∫xe3x2dx, I2=∫1.dx Then, I2=x Let fx=xe3x2

Q: 10.S 2 x3 x+1 dx

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 8x dx 1) Jo 4x2-5 ex 2) S², dx -1 1+ex L,4-* In 2 dx

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: •0.6 x² -dx V9 – 25x2 0,

A: …

Q: Evaluate the definite integral using the given values

A: Given that ∫26x3dx=320,    ∫26xdx=16,   ∫26dx=4. Consider the integral ∫262x3-10x+7dx. Evaluate as…

Q: 1.Jx' dx 2.1-dx X 3.18x²dx

A: Topic = Derivative

Q: -3 -dx J2 (x²–1)² 3.

A: The given integral,        ∫23xx2-12dx

Q: 1. [(4-x) dx. -2

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3. Differentiate y = 2x-1 - with respect to x and then evaluate 2 x(x – 1) -dx (2x – 1)2

A: Given and

Q: 1 = S V1- xV3+ x dx %3D

A: Use integration by part

Q: 4 sec*(x) rind tha ualı Find the value of ((x* - 5x² – 6x)“ 4x³ - 10x – 6 dx. (x4–5x²–6x)* - a) 4…

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Q: dx 2. S; x²-4x+5

A:

Q: X 3- Ssin ² x dx ។

A:

Q: b) Integrate: 2x + 5 -dx 2x*(x+3)(x –1)

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Q: 2 S (x² – 4| – |æ – 1)) dæ - 4| – |x – 1|) dx -2

A: Definite integration

Q: 6. J 4 x4-1 -dx

A:

Q: Differentiate the function. (2x + 3)5 y = (4x + 1) dy dx

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Q: 2х+2 dx. 5. J2-2x+1 х2-2х+1

A: Given that a integration and we solve this integration by using general formulas of integration. We…

Q: Sx² cosh (1-x³) dx

A: Let the given integral be I - I = ∫x2cosh1-x3dx                   ............(1)Let,t = 1-x3…

Q: 3 9 dx dt -1 -3 [:] 2 with a (0) = 4

A:

Q: 2-x dr = - tn(4x* + 4x - 3) + 4x² + 4x – 3 16 (x + 3)*(x – 1)^ | F(x+2)* x+1 (x+ 3)(x + 2)(x – 1)…

A:

Q: (x + 1)2 + y = Inx; y(1) = 4 dx Oyx + 1) = xlnx – x + 9 Oyx + 1) = xlnx – x + 8 Oyx + 1) = xlnx – x…

A:

Q: 2 の x3 ex lx の 2X dx to

A: 3 Given: ∫12x3ex dx   ……1

Q: X 10. [7x+3x+1 dx 2x ux 11. Jhxdx 12. f(x²-4)³ dx 2x

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Q: Differentiate the function. y =    3x2 + 2x + 5  dy dx =

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Q: 9. S." §, x*V9-x dx 16 dx Vx-2 10.

A: We need to evaluate the given definite integrals, to sove we will use the substitution method.

Q: | x(x – 2) sech(2x²e¬x) dx ex

A: To find: ∫xx-2sech2x2e-xexdx

Q: x² 1 arctan 16 2(x – 3) + 3 -dx = J (2x² – 6x + 13)² + c 2 x² – 6x + 13

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Q: 18) fvī dx 19) f se'de 3e dx 20) (3x - V5x + 2) dx

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 5. j(4x²-5x+4)*(8x-5)dx 6X dx x ²-5

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Q: 1 dx oraz 1 dx. 1+ x² Oblicz 1+ x²

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Q: 10 ii) J1 x(10+lnx)3 dx

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Q: ∫[(1/ (x2√(4 - x2))) dx] Please show all work

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Q: Differentiate. (x + 1)4 y = In ex-3 d (x + 1)4 In dx ex-3 %3D II

A: Given:-  To differentiate w.r.t. x

Q: 3 dx 4. = 2/3 V3-x 0,

A: Solve the problem by substitution. Substitute 3-x=t

Q: 3x + 1 dx 28. V4 – x2 -

A: Formula used : ∫dx1-x2=arcsin(x)+c

Q: Sel+x3/2 Vx dx ,1+3 X,

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Q: 4 V2x + 1 dx = || 1 dx 3= %3D 1+x2 -1

A: Given: a)   ∫042x+1dxb)   ∫-11xx2+1dx

Q: 4. S(5x +) dx = dx = 2 5. S- x7 x4- 15x6 6. S (四 극) dx %3D

A:

Q: 4. S Vä(x² + 2) dx 5. S(-3 Vã – 6x v7) dx 6. (9x*-6x²+7x²-5x+15 dx 3x

A: