INTEGRALS INVOLVING QUADRATIC EXPRESSIONS

(1)  Evaluate the following with respect to "x".

(2x - 3) / (x² + 4x - 12)      Solution

(2)  Evaluate the following with respect to "x".

(5x - 2) / (2 + 2x + x²)    Solution

(3)  Evaluate the following with respect to "x".

(3x + 1) / (2x² - 2x + 3)    Solution

(4)  Evaluate the following with respect to "x".

(2x + 1) / √(9 + 4x - x²)      Solution

(5)  Evaluate the following with respect to "x".

(x + 2) / √(x² - 1)        Solution

(6)  Evaluate the following with respect to "x".

(2x + 3) / √(x² + 4x + 1)       Solution

Integration with Quadratic Expression in Square Root

(1)  Evaluate the following with respect to "x".

 √(x² + 2x + 10)          Solution

(2)  Evaluate the following with respect to "x".

 √(x² - 2x - 3)         Solution

(3)  Evaluate the following with respect to "x".

 √(6 - x)(x - 4)         Solution

(4)  Evaluate the following with respect to "x".

 √[9 - (2x + 5)²]         Solution

(5)  Evaluate the following with respect to "x".

 √[81 + (2x + 1)²]            Solution

(6)  Evaluate the following with respect to "x".

 √[(x + 1)² - 4]         Solution

Integrals with Quadratic Expression in Denominator

(1)  Integrate the following with respect to x:

1/[(x + 1)² - 25]            Solution

(2)  Integrate the following with respect to x:

1/√(x² + 4x + 2)           Solution

(3)  Integrate the following with respect to x:

1/√((2+x)² - 1)           Solution

(4)  Integrate the following with respect to x:

1/√(x² - 4x + 5)           Solution

(5)  Integrate the following with respect to x:

1/√(9 + 8x - x²)           Solution

(6)  Integrate the following with respect to x:

1/[(x + 1)² - 25]        Solution

(7)  Integrate the following with respect to x:

1/√(x² + 4x + 2)        Solution

(8)  Integrate the following with respect to x:

1/√((2+x)² - 1)        Solution

(9)  Integrate the following with respect to x:

1/√(x² - 4x + 5)        Solution

(10)  Integrate the following with respect to x:

1/√(9 + 8x - x²)        Solution

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