h(x) da (In(x), d

Q: d -(3x² + 11)e¬ª at x = –1. dx Evaluate

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Q: C = dx (1- x²)) X tanh-1 %3D

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: a-) I = c6 Vx²-9 dx 3 b-) S x In(x² + 1) dx

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: x- /= ² + √²-11 de dx dx x-1 x² + x + 1 3

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Q: dx 0 4-x

A: To evaluate the integration.

Q: (e + x + 2)dx 3.

A: The sum rule for integration states that ∫fx+gxdx=∫fxdx+∫gxdx. The integration formula for…

Q: Find the derivative of f(x)

A: Using the product rule,

Q: H-w 2x +3 dx メ+2 X X 3 X2+ 2X+1

A: Topic:- application of integration

Q: d -[x*] = xx"-1 dx

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

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Q: e. x3 √1+x4 f. fx sin x² dx S dx

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Q: dx i let x-= 4X-X2

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Q: d x4 – 5x? + 7 dx x2 + 1

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Q: d) х =dx Vx² +1 - (Inx)* -dx

A: We use substitution method

Q: g. In x*dx

A: g)

Q: Using integrating factor, solve dy/dx - 2xy = x

A: The objective is to solve the differential equation dydx-2xy=x.

Q: defferentiate the function: y= ln((x^1/3)/(2x+1))

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Q: y= ln (e^-x + xe^-x) y'=

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Q: αdx = x x2-a2 dy

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Q: 2tan-(x) dx = (e)None In2 In4 In2 In4

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Q: 2x (x-a)² dx; a is constant

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Q: a. S f (x² - 2x + 1) e²x dx

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Q: 7. f* (x² + 8) & dx CO (³ (x-1)

A: We have to solve integral

Q: x dx 5. J 3-x2-6x

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Q: -1)/(x4))1/2

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Q: x+2 a) f- =dx V2x-x² |xIn(x+1)dx b)

A: Given that  (a) ∫(x+2)/√(2x-x2) dx   (b) ∫x ln(x+1)dx Here we have to calculate the given integral.

Q: f (x) = x² ln x

A: Given function:-     f(x) = x2 lnx

Q: 3 - dx x² – x - 2 (1) (ii) fx'e* dx

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Q: e" sin x = x- xy S1

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Q: • S (++:) (- 1 x2 – 1 dx - x2

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Q: x2 dx zX - biN 円-X

A: We will use substitution to solve this

Q: d (sin²(x)e³*+") dx xp

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only the first…

Q: 3- x 3) dx → S2xe* dx

A: To evaluate the given integrals.

Q: dx 4-x とt

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Q: f(x) = (2x2 – 5x)ln(x² – x) f'(x) = ?

A: Product Rule ddx(h(x)g(x))=ddx(h(x))g(x)+h(x)ddx(g(x)) Chain Rule ddx(h(g(x)))=ddhu(h(u))ddx(g(x))…

Q: xペ-SX dx x2

A:

Q: cosh x dx е e- 2х

A: Given integral is ∫coshxe-2xdx

Q: x*dx 3. S x2-1

A: use a partial fraction to solve the integral.

Q: (4(x2-1) dx x²(x+2)

A: We will use partial fraction here

Q: | (e-x + vx)dx 1. 2. x²)dx

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Q: s e8*(x³ + x²)sec² (x*e3* + 1) dx

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Q: ľ V2x + I dx S" x e*-1 dx

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Q: e* - x e* et dx = 2x2 + constant 2 х

A: To show that∫ex-xex2x2dx=-ex2x+constant

Q: solve for y in terms of t or x, as appropriate ln (y - 1) - ln 2 = x + ln x

A: Given equation, lny-1-ln2=x+lnx

Q: x-1 dx 2xーx

A:

Q: dx dx 3. x1

A: Given ∫dxx3-dxx

Q: F(x) = ln(x), [1,3]

A: The given function is: f(x)=ln(x) ;         x∈1, 3