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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OTHER TOPICS 

Profit and loss shortcuts

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Domain and range of rational functions

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Graphing rational functions

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Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6