2. Prove that d [(2x+1)³] (2x+1)³(4x-19) (x-3)² dx = Then, -5 (2x+1)(8x-38) 3(x-3)² dx.

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A:

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A: Thus the integration is a process of finding anti derivative of a function . There are basically two…

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A: Given integral is      (1) Its reduction is ∫Ax+Bx2+1+C(3x+2)+D9x2+12x+16dx We can write it as…

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A:

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A: Let's find.

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A:

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A:

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A:

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A:

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A:

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A: Find the derivative of the given function.

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Q: If x = (1/2)a + (2/3)b + (3/4)c c=(12x-6a-

A: The detailed solution is given below Thank you

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A:

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A: We have to solve above question  And find integral

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A: We will solve the problem

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A:

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A:

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A:

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A:

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A:

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A: A differential equation of type   P(x,y)dx+Q(x,y)dy=0   is called an exact differential equation…

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A: Solve the following integration

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A: Follow the procedure given below.

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A:

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A: the given integral is (4x2+x-3)/(2x2-3x-2).

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A: Given integral: We have to evaluate the given integral.

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A:

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A: C+C

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A:

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A:

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A:

Q: (9) f(x² - & 8x + 3)dx (h) f(ax + + b)dx ff f(²x² (i) 7x + 4e -3dx

A: Here we have to find the integration using basic properties.   Part- g Now, ∫(x2-8x+3)dx=∫x2 dx-8 ∫x…