1) Evaluate the following (general) antiderivatives: a)[9x' +7x+4 dx = b)J9 cos(x)+8sin(x)+7e* +6sec²(x)+-_3 1+x 4 dx =

Q: Find the antiderivative of 5sin x In5 cos x dx 5coS x + C 5sin x In 5 + C O sin x + C In 5 5sin x +…

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Q: Find the antiderivative of: x*+1 (n+ 1)2 [(n + 1) In x – 1] if n± -1 x* In x dx = z (In x)² + c if n…

A: Find the anti derivative.

Q: We have determined that du = 5x* dx. However, the given indefinite integral dx does not conta %3D x…

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Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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Q: 4 3 12 2 cos (x2) 3Vz Evaluate the integral|| dx dy dz by changing the order of integration in an…

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Q: 1. Find the following antiderivatives. (a) [² cosh x + 1 sinhx dx

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Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy

A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy

Q: 6. Let a be a positive constant. Determine the general antiderivative of a using the fact 1 a² + x2…

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Q: 5) Find the general antiderivatives for the following; х-1 dx x* +2х-3 -dx 6)

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Q: 1: Evaluate the integral 3x - 1 (x + 4)(2x - 1) I -dx.

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Q: 1) y = 2sin (5x) ,2) y = In x'n cosh 5x ,3) xsin=14y = y tan-14x 4) y = ecosh (8x),5) y =- t +1 t…

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other question as…

Q: 1. S 5e* dx 2. S(2 – 3e*) dx 3. S 72x+3 dx 4. S dx x In x 3 dy 5. S 4y-3 6. S dx 2 x+5 7. Se* (1 +…

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Q: 1 7. Evaluate the integral -dx using Simpson's method and also find the error comparing ó x +9 with…

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Q: 13. Evaluate the indefinite integral fx cos x dx x sin 2x cos 2x a. + c 2 x sin 2x cos 4x b. + c 2 2…

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Q: The integrating factor µ(x) of the differential equation: dy (x In x) + y = 2 In æ is In x H(x) =…

A: Integrating factor is lnx see the step 2

Q: Pind the derivativa otthe Pollowing の3=2 Sin'Csx) In coshラX 3 =\nx (3) Xsin 4y=Jtan YX

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Q: 1.1 the integral f cos(lnx) dx . x2 1.2 the integral S x³V1– 2x dx

A: 1.1 Given integral is ∫coslnxx2dx Let u=lnx⇒dudx=1x dx=xdu1x=e-u∫e-ucosudu we will integrate by…

Q: Find the antiderivative of dx / (25 + 4 x^2) * O (1/2) arctan (x/5) + C O (1/10) arctan (2x/5) + C O…

A: An antiderivative is an integral process that can help a function to get back into its parent…

Q: Find the most general antiderivative. 4 9 dx 4 sin-1 x - In Ixl +C 4 sin-1 x + 9 In |x| +C 3.…

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Q: Find the most general antiderivative (a) Integral [ (cos(ln x)) / x ] dx (b) Integral [ (x2)(ex^3)…

A: Given (a) ∫coslnxxdx  (b) ∫x2ex3dx  We have to find the most general antiderivative.

Q: 1.) Find the equation of the line tangent to f(x) = 6 ln(7– 3x)+5e-4 – 6x – 2 at x = 2 2.) Find the…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Evaluate the integral: e3+cosh2x33+cosh2xsinh2x dx (Α) (3e)3+ sinh2x 2+In3 + C (3e)3+cosh2x B 2+2ln3…

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Q: Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx A (3e)3+ sinh2x 2+In3 +C (3e)3+cosh2x B) 2+2ln3…

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Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 3. The integration of x e* with respect to x is: A. e2x. В. 2хе* С. 2

A: To integrate  xex2 with respect to x: ∫ xex2dx Apply u-substitution: u=x2 Differentiate both sides:…

Q: Find the general form of the antiderivative of g(x) = - cos4x

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Q: 1. Evaluate the integral r4-x² 8x cos Y dy dx Y – 4 by reversing the order of integration.

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Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

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Q: It can be shown that y, = 2 and y, = cos²(9x) + sin²(9x) are solutions to the differential equation…

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Q: 1. Evaluate S x³V1+ x² dx using Integration by parts.

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Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: 4. Determine the following indefinite integrals: a) S(2x + 3x -7x2 + x-5) dx %3| b) S(x – 5)² dx g)…

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Q: find (In x)³ dx 2x In (In x) dx x In x 11. 12. In9 et/2 dx tan x In (cos x) dx 13. 14. In4 eVi cdr…

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Q: Find the antiderivative of 5$sinx ln 5 cos x dx. A.) 5cosx + C B.) 5sinx + C C.) 5sinx In 5 + C 5sin…

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Q: Compute the general antiderivative S a"-1 cos(x")dx COS where n > 1 is an integer greater than 1.

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Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: 10х> — 5х For the integral -dx , if u = x*-x2+6 then Mdu = (10x³-5x)dx, what is %3D x4-x²+6 M?

A: We have integral ∫10x3-5xx4-x2+6dxifu=x4-x2+6

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: Evaluate the integral: e3+ cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 + C (3e)3+cosh2x B 2ln3…

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Q: 2. a) Evalute the following improper integrals dx Vx – 3

A: We will solve the problem.

Q: 11) e3x = sin(x + 8y) %3D dy A) - dx 3ex 8sin(x + 8y) 24ex dy B) dx sin(x + 8y) dy sin(x + 8y) -3ex…

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Q: When the group of terms in a first-order DE contains y dx + x dy , the following integrating factors…

A: Integrating factor is a function used to solve differential equations. It is a function in which an…

Q: 1) Find the indefinite integral S(3x* – 6vx + 3 cos x – 4e*)dx. 2) Find S 4(sin(6 sin x + x² + Vx))…

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Q: 10. * S sin(In x)dx 1 C x sin(Inx) – cos(Inx) + C 2. x sin(Inx) – cos(lnx) + C 1 x sin(lnx) +…

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Q: 3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C…

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Q: Activity 5: Find the following indefinite integrals. 1. Sdy 2. fx(8x? – 6 +) dx 3 6. S COSX dx sin?x…

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