Algebraic integrals:
Integrals of form:
![2118_Algebraic integrals.png](https://www.expertsmind.com/../CMSImages/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
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
.
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](https://www.expertsmind.com/CMSImages/723_Algebraic%20integrals5.png)
Now I =
![1152_Algebraic integrals3.png](https://www.expertsmind.com/../CMSImages/1152_Algebraic integrals3.png)
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