e-t sin(v3t) dt (a) L

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A: y=sinxe-x. Then we have to find desin-1ydlnx.

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A: To evaluate the given definite integral

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Q: Find dy/dx

A: The given expression is:

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Q: Original Sound ff EXERCISE dy -x = x2 siny dy 3 -(-siny ANSWER: X = %3D

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A:

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A: Integrate by substitution

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A: We will apply Leibnitz theorem to solve it

Q: 2x^ + xt3 dx x+ x a. In lxl+Ź In Cx t1)+ tan-"c) tc b. In \xl-Į m (x2+1)+ tan-' Cx) tc in e, wone

A: The integration of the integral is  (2x2+x+3)/(x3+x).

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A:

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A:

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A: Here, we will differentiate  siny dx+x-sin2ydy=0....(1)

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A: Take the integral: integral e^(-3 t) t sin(2 t) dtFor the integrand e^(-3 t) t sin(2 t), integrate…

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A:

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A: Given that, f(x,y)=xcosy-ycosx1+sinx+siny The derivative with respect to x is,…

Q: dx i- xIn x cox + sin x dx. cos x- sin x i.

A: (i) The given integral is ∫1x ln x dx. Let u=ln x. Then du=1xdx. Apply the substitutions and…

Q: L {t®e-%t} L{e-t cos 2t} L {2e3t sin 4t}

A:

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A: Use the concept of derivative of an Antiderivative.

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A: The solution attached :

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A:

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A: The LHS of the given equation is cosx+y-cosx-y. Note that, cosA+B=cosAcosB-sinAsinB and…

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A: Given

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A: Answer is mentioned below

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A: We need to evaluate ∫ex sec2(ex+1) dxtan(ex+1)                              (1) Let tan(ex+1) = t On…

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A: To find the below integral. ft=∫0te−tsin2tdt

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A: