Calculating indefinite integrals

In summary, an indefinite integral is a mathematical concept used in calculus to find the antiderivative of a given function. To calculate an indefinite integral, various integration techniques can be used such as substitution, integration by parts, or partial fractions. Unlike indefinite integrals, definite integrals have specific upper and lower limits and give a single value as the result. There is no definite rule to determine if an indefinite integral is solvable, but having a good understanding of integration techniques and practicing solving different types of integrals can help. Common mistakes when calculating indefinite integrals include forgetting to add the constant of integration, making algebraic errors, and forgetting to replace variables after substitution. It is important to double-check solutions by differentiating them to ensure they are
  • #1
Cacophony
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0

Homework Statement


a) S 13(4^x + 3^x)dx
b) S (cosx + sec^2x)dx
c) S (3-(1/x))dx
d) S e^(7x)dx


Homework Equations



The S is supposed to be the integration sign

The Attempt at a Solution



Are these correct or at least close?

a) = 13((4^x)/(ln(4) + (3^x)/(ln(3))) + C

b) = (sinx + tanx) + C

c) = -ln + C

d) Do I use U-substitution for this one?
 
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  • #2
c) and d) are incorrect. The integral of "3" is "3x". For d), yes, use substitution. Let u= 7x.
 

1. What is an indefinite integral?

An indefinite integral is a mathematical concept used in calculus to find the antiderivative of a given function. It is represented by the symbol ∫, and it is the inverse operation of differentiation.

2. How do you calculate an indefinite integral?

To calculate an indefinite integral, you need to use integration techniques such as substitution, integration by parts, or partial fractions. You can also use tables or computer software to help with the calculations.

3. What is the difference between indefinite and definite integrals?

An indefinite integral does not have upper and lower limits, while a definite integral has specific values for the upper and lower limits. Indefinite integrals represent a family of functions, while definite integrals give a single value as the result.

4. How do you know if an indefinite integral is solvable?

There is no definite rule to determine if an indefinite integral is solvable, but there are some techniques and methods that can be used to solve most integrals. It is important to have a good understanding of integration techniques and practice solving different types of integrals.

5. What are some common mistakes when calculating indefinite integrals?

Some common mistakes when calculating indefinite integrals include forgetting to add the constant of integration, making errors in algebraic manipulations, and forgetting to replace the variable with the correct value after substitution. It is also important to double-check the solution by differentiating it to ensure it is the correct antiderivative.

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