Algebraic integrals Assignment Help

Assignment Help: >> Indefinite integral >> Algebraic integrals

Algebraic integrals:

Integrals of form:

 2118_Algebraic integrals.png

In such type of integrals we write px + q = l (diff coefficient of ax2 + bx + c) + m.

Find l and m by comparing coefficient of x and constant term on both sides of identity. In this way question will reduce to the sum of 2 integrals which can be easily integrated.

Integral of the type 1677_Algebraic integrals1.png 

In this case substitute ax2 + bx + c = M (px2 + qx + r) + N (2px + q) + R

Find out M, N, & R. The integration reduces to integration of 3 independent functions.

 

Example: Evaluate 750_Algebraic integrals2.png.

 

Solution:        Let x + 1 = (differential Coefficient of 2x2 + x - 3) + B

                         x +1 = A(4x + 1) + B = 4ax + A + B

                        equating coefficients,  723_Algebraic integrals5.png

                        Now I = 989_Algebraic integrals4.png     

                        1152_Algebraic integrals3.png

 

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