Integration of the Irrational Algebraic Fractions:

1. Irrational functions of (ax+b)^1/n  and x can be evaluated easily by substitution

tⁿ = ax+ b. Thus .

2.  . Here we substitute, x -k = 1/t.

This substitution will reduce  given integral to  . 

3.          we first put x=1/t, so that

.

Now the substitution C + Dt² = u² reduces it to the form .

4.

Here, ax² +bx  +c  = A₁ (dx +e) ( 2fx +g) +B₁( dx +e) +C₁

here A₁, B₁ and C₁ are constants which can be attained by comparing the coefficient of  like terms on both the sides. And given integral will reduce to form

Example: Evaluate .

Solution:  Put x + 1 = t², we get 

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