Find the general antiderivative of f Cx) = 7x end check the Lons answer by differentiating.

Q: Use a substitution to reduce the ODE to a separable type and then solve it: dy x+y dx x-y

A: To solve the given ordinary differential equation (ODE) dydx=x+yx−y, it can use a substitution to…

Q: Use your answer in (a) to find the general antiderivative of f

A: The given function fx=3x5+13x-4x8 We have to write the function in exponential form and use it to…

Q: (a) / #(8+ 2²) dz = +C. -3x6 + 6x12 dx = (b) +C. -3 (c) / (6 + x*)² dx = +C.

A: Explanation of the answer is as follows

Q: Find the antiderivativef e* sinxdx A.je*(sinx – cosx) + c C. e*(sinx — cosx) + c Find the…

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Q: Describe the set of antiderivatives of ƒ(x) = 0.

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Q: S(8x3 + x-3)dx

A: Solve by integration

Q: Evaluate the following antiderivatives: See pictures below

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Q: dy a) Find in terms of y, if x= e* in terms of y, if x= e*+Insin y dx

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Q: +x 5) Let z = f(x² – y²). Show that y ду əx az

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Q: nd the antiderivative x² + 2x -dr. (r² + 1)'

A: Put x2=t then integrate.

Q: Find all local extrema for 4 f(x, y): * - 4xy + y.

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Q: (Wh(2 - h)dh

A: To evaluate: ∫(h(2−h)dh Let I= ∫2h12−h32dh

Q: | sec 5x dx

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Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: 1. 3 de

A: Given integral,         ∫3 dx

Q: What is the most general antiderivative of

A: Consider the expression x4+x+1x. We have to find the antiderivative of the above expression. For…

Q: |2²+2x + 1 dx

A: