Solve 8(t-nt)cos () dt.

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A: We will solve the problem.

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A: Given a(t)=cos t Integrating with respect to t to get velocity function, vt=∫atdtvt=∫cos t…

Q: (t² +3) cos(5t) dt

A: According to integration by parts:∫udv = uv _ ∫vduWhere u can be choose in the orderInverse, Log,…

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A: Since you have asked multiple questions in single request so we  will be answering only first…

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A: ∫0π/2 cos9tdt ∫0π/2 cost(1-sin2t )4dt here lets substitute that sint = u du/dt = cost du = costdt…

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A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx…

Q: differential

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A: Differentiating with respect to t, we get

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A: We have given,