We will compute indefinite Integrals

Basic Indefinite Integrals

We now present a list of basic indefinite integrals. In this context, the word basic means that the formula shown comes directly from its corresponding differentiation formula.

1.
Constant functions: where is any constant.
2.
Power functions ():
3.
Power functions ():
4.
Trigonometric functions:
a.
b.
c.
d.
e.
f.
5.
Natural exponential function:
6.
General exponential function: where .
7.
Inverse trigonometric functions:
a.
b.

Minor modifications

In many applications, the independent variable is multiplied by a constant, . We list the effects of such a modification on indefinite integrals.

8.
9.
10.
11.
12.
13.

Problems

(problem 1) Compute

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(problem 2) Compute
The answer is a minor modification of

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(problem 3) Compute

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(problem 4) Compute
The answer is a minor modification of

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(problem 5) Compute

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(problem 6) Compute

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(problem 7) Compute
The answer is a minor modification of

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(problem 8) Compute
The answer is a minor modification of

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(problem 9) Compute

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(problem 10) Compute
Note that the variable is
Write your answer as to a power.

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(problem 11) Compute
Note that the variable is

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(problem 12) Compute
Note that the variable is

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(problem 13) Compute
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 14) Compute
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 15) Compute
Use the Power Rule with
The Power Rule says C
Note that the variable is

Do not add the +C to your answer

(problem 16) Compute
Use the Power Rule with
The Power Rule says C
Note that the variable is

Do not add the +C to your answer

(problem 17) Compute
Use the Power Rule with
The Power Rule says C
Note that the variable is

Do not add the +C to your answer

(problem 18) Compute
Use the Power Rule with
The Power Rule says C
Note that the variable is

Do not add the +C to your answer

(problem 19) Compute
Rational exponents:
Use the Power Rule with
The Power Rule says C

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(problem 20) Compute
Rational exponents:
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 21) Compute
Negative exponents:
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 22) Compute
Negative exponents:
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 23) Compute
Negative rational exponents:
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 24) Compute
Negative rational exponents:
Use the Power Rule with
The Power Rule says C

Do not add the +C to your answer

(problem 25) Compute
Negative exponents:
The Power Rule does not apply when
Recall

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