HOW TO INTEGRATE INTEGRAL WITH SQUARE ROOT IN NUMERATOR
Let us find out the Integration of quadratic polynomial in denominator, integral of square root of polynomial, integrals with square roots in denominator, integration of linear by quadratic, integral with square root in numerator ,integration of square root formula .
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Let us take some examples to integrate such type of example.
Problem
1st of all making the co eff off x^{2} positive and unity if it is not and then rewrite x^{2} +4x 1 as sum/difference of (a + b )^{2 } = a^{2} +b^{2} åœŸ2ab
Now write the remaining term to equalise x^{2} + 4x 1,
Now writing the last term as square root of term and then multiplying the co eff of x^{2} with ve sign which was earlier taken outside .
Now use the formula written below

Here in this case 'x' will be replaced by 'x + 2' and 'a' will be replaced by √5
Where 'c' is called constant of integration.
This video will explains very easy and short method of such types of integration
Problem
1st of all making the co eff off x^{2} positive and unity if it is not and then rewrite 2x^{2} + x  1 as sum / difference of (a + b )^{2 } = a^{2} +b^{2} åœŸ2ab
and c^{2} as follows :
2x^{2} + x 1 = 2[ (x )^{2} + 2× (1/4)(x) +(1/4)^{2}  (1/4)^{2} 1/2]
2x^{2} + x 1 = 2[ {(x)^{2} + 2 (1/4)(x) +(1/4)^{2}} {(1/4)^{2} +1/2}]
= 2[{(x) + (1/4)}^{2}  {1/16+1/2}]
= 2 [{(x) + (1/4)}^{2}  {9/16}]
= 2[{(x) + (1/4)}^{2}  {3/4}^{2} ]
Now using the Result
The integration of this Integrand can be written as follows
Where 'c' is called constant of integration.
Now multiplying with 2 all the terms and After simplification we shall have
In this post we discussed Integration of quadratic polynomial in denominator,integral of square root of polynomial,integrals with square roots in denominator, integration of linear by quadratic, integral with square root in numerator ,integration of square root formula,integration of square root formula,integral of root 2, anti derivative rules for square roots Please like it and share this post with yours friends.
Also Read How to learn trigonometric identities easily
Also Read How to learn trigonometric identities easily
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