Formulas of Integral - I
1. Constant Integral
-> the integral states the constant is the constant multiplied by the integration's variable.
Formula:
2. Power Integral
-> the integral states the xn where n is not equal to -1 plus the the integration's constant.
Formula:
3. Integral of a Function with Respect to Itself
-> the integral states the function with respect to its own variable, when the function is the variable itself, plus the integration's constant.
Formula:
4. Sum Integral
-> the integral states the sum or difference of a functions is the integration's sum or difference.
Formula:
5. Product and Constant Product Integral
-> the integral states the usage of integration by parts.
Formula:
6. Quotient and Constant Quotient Integral
-> the integral states the usage of integration by substitution or partial fraction.
Formula:
7. Square Root Integral
-> the integral states the square root of a function can be found by using substitution.
Formula:
Example |
1. Find the answer from this given:
Steps:
a. Write the given 1st.
b. Use the specific integral formula.
c. Find the integral.
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= C = 5
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Exercises |
1. 
Steps:
a. Write the given 1st.
b. Use the specific integral formula.
c. Find the integral.
Solution:
=
= Formula: ;
=
= c1 = 3; c2 = 4; n1 = 2; n1 + 1 = 3; n2 = 1; n2 +1 = 2
= ;
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= 
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Answer:
2. 
Steps:
a. Write the given 1st.
b. Use the specific integral formula.
c. Find the integral.
Solution:
=
= Formula: ;
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= u = x2 - 5; du = 2x dx;
= Use to substitute the given: 
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=
= 
= Substitute the u.
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Answer:
3. 
Steps:
a. Write the given 1st.
b. Use the specific integral formula.
c. Find the integral.
Solution:
=
= Formula: ;
= Use to substitute the given: 
= 
= 
= 
= Substitute the u.
= 
= 
Answer:
4. 
Steps:
a. Write the given 1st.
b. Use the specific integral formula.
c. Find the integral.
Solution:
=
= Formula:
= c = 5; n = 1; n + 1 = 2
= ;
= 
= 
Answer:
5. 
Steps:
a. Write the given 1st.
b. Use the specific integral formula.
c. Find the integral.
Solution:
=
= Formula: ;
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= 
= 
= 
Answer: