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homeworkjunk
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Homework Statement
[tex]\int \frac{6^x+12^x}{2^x}dx[/tex]
Homework Equations
[tex]\int a^udu= \frac{a^u}{ln a} +C[/tex]
The Attempt at a Solution
I don't know where to begin, I tried using parts but gave up.
An exponent in a simple integral is a small number written above and to the right of a larger number, which indicates how many times the larger number should be multiplied by itself. In the context of integrals, exponents are used to represent repeated multiplication of a variable by itself.
To solve an integral with exponents, you can use the power rule, which states that the integral of x^n is equal to (x^(n+1))/(n+1) + C, where C is the constant of integration. This rule can be applied to each term in the integral separately.
Yes, the power rule can be used for any type of exponent, whether it is a positive integer, negative integer, fraction, or decimal. However, if the exponent is a negative integer, the resulting integral will contain absolute value bars.
Yes, there are other rules that can be used to solve integrals with exponents, such as the substitution rule, the product rule, and the quotient rule. These rules can be useful for more complex integrals with multiple terms or variables.
Yes, there are many online calculators and software programs that can solve integrals with exponents for you. However, it is important to have a basic understanding of the rules and concepts involved in solving integrals with exponents in order to use these tools effectively.