Find dly/dx y = Xu15て 1t. y = 12x5%3 9

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A: We can use method of substitution in order to solve the given problem.

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A: Solution for Q no 8 in given in the next step:

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A: Consider the given definite integral.

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A: ∫ (x+3)dx/(6x-x2) ∫ (x+3)dx/x(6-x)  -∫ (3/2(x-6) - 1/2x) dx  -3/2∫ dx/x-6 + 1/2∫dx/x {ln(x) -…

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Q: 5. L.V4– 2x dx dx 5x+2 6.

A: Topic = Integration

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A: 2π∫02x21+4x2 dxlet x=tan u2dx=sec2u2du=2π∫14 tan2 u1+tan2u·sec2u2 du=π4∫sec2u  tan2 usec2u  du…

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A: As per your request I will solve d part

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A: Integration by parts: ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx   We have to evaluate ∫x e-2x dx.

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A: here we use the log rule  ∫ 1/x dx = log(x)  and , find the indefinite integral .

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Q: 7.) L13x + 1|dx

A: Since you have posted more than one question, we solve the first one for you. For the remaining…