Differentiate J(1+x"

Q: Find the implicet differentiation x3y3-y=x

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

A: Topic = Integration

Q: Evaluate the integral.

A: Given integral is We will use the following substitution to evaluate the integral.

Q: 3. Use the Fundamental Theorem of Calculus to evaluate the definite integral 16 x Vx dx 4

A: Given: ∫416xxdx Simplifing the given integral∫416xxdx=∫416x(x12)dx                 =∫416x1+12dx…

Q: +1 dx. (x+3:2-5)3

A: To evaluate  ∫x2+1x3+3x-53dx

Q: x-3(x-1 + x)²dx

A: Given, ∫x-3x-1+x2dx It is required to evaluate the integral.

Q: x dx |-7-8X-x²

A: This question can be solved using the concept of some special integrals.

Q: Verify whether the function g(x) solution of the integral equation R P daft

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Q: Evaluate the integral.

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Q: Evaluate the integral. x sec2(8x) dx = +C

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Q: Express f(x) by the Fourier integral where f(x) = - 2, -3< * < 3 otherwise. %3D

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Q: Evaluate the integral. x sec (9x) dx +C

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Q: (x-1)?

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Q: 1. fx³ In x dx

A: Evaluate the integral equation by integration by parts .

Q: Solve for f(x) the integra 1

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Q: Verify the MVT for f (x) = ln x on [1, 4].

A: f(x)=lnx is continuous in the interval [1,4] f'(x) = 1/x is also continuous on (1,4) So f(x)…

Q: Evaluate the integral: / (3x+5)dx x²+2x+1

A: ..............(1)

Q: Verify the statement by showing that the derivative of the right side is equal to the integrand on…

A: We will find the derivative of right side. By showing this derivative equal to integrand the…

Q: Evaluate the integral: (x-1)?

A: Given, ∫02(x-1)e(x-1)2dx To evaluate the integral.

Q: x+3 x+1

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Q: 4. Express f(x) by the Fourier integral where f(x)= (-2, -3< x < 3 otherwise.

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Q: Evaluate the integral. 3. x² + x + 1 dx Jo (x + 1)2(x + 2)

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Q: Find the antiderivative of x/sqrt (x2+1) and verify it by differentiation?

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Q: Find the integral. x° -7 dp-

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Q: Evaluate the integral x Cx²-3) dx

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Q: Evaluate the integral ∫x√x+1dx.

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Q: Evaluate the integral x/dx 2.

A: The collection of all antiderivative of f is called the indefinite integralof f with respect to x,…

Q: Evaluate the integral. J1/v3 1 + x² xp

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Find the integration of function b a) S[secx 2tanx3 csc25x -

A: We have to find the given integrations

Q: 3x 2.5 dx V1 — 5х2

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

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Q: 2x* dx

A: Here is the solution

Q: The integral of (x-1)(x+1)^(1/2)

A: Given,

Q: Evaluate the integral. '5 x - 4 dx x2 - 3x - 18

A: We first factor the denominator. ∫-25x-4x2-3x-18dx=∫-25x-4(x-6)(x+3)dx

Q: Evaluate the integral. r5 x3 – 3x² – 9 dx J4 x3 – 3x²

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Q: Q2)- Evaluate the integ 2x+5 S dx 1.

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Q: Evaluate the integral.

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Q: Evaluate the integral. (2x2 dx +X +

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Q: Evaluate the integral. dx g4 Vx² + 3

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Q: Evaluate the integral f(4x³ + 5x* + 2)dx

A: ∫xn dx xn+1n+1+C ∫a dx ax + C

Q: Evaluate the integral. (7x + 2) dx x2 + 4

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Q: Find y ' by implicit differentiation for 4x² y7 – 2x = x5 + 4y3 . %3D

A: We have to find y' by implicit differentiation of : 4x2y7 - 2x = x5 + 4y3

Q: Find the integral ∫x / √x+1dx.

A: Given the integral

Q: 1+x

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Q: |x| dx 1–x²

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Q: Evaluate the integral.

A: Integral:∫2xxdxLet, x=z      12x dx=dz

Q: Evaluate the integral. x sec (8x) dx + C

A: