Integral (maybe simple maybe hard)

In summary, the conversation discusses a problem with finding the integral of (t^2)/(1+2t) and suggests using a u-substitution to solve it. However, the attempt at a solution did not work and other methods, such as integration by parts, were also unsuccessful. It is suggested to try splitting the integrand into easier parts by long division.
  • #1
hello.world
1
0

Homework Statement


integrate (t^2) / (1+2t) . Wolfram alpha gave this as the answer: http://www4a.wolframalpha.com/Calculate/MSP/MSP957620di145hih25dggd00002hc5g230hb2h25hd?MSPStoreType=image/gif&s=24&w=229.&h=36. [Broken]

The Attempt at a Solution



I tried a u-substitution and couldn't arrive at a solution. Any other suggestions! Int by parts doesn't seem to work either!
 
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  • #2
The only easy method that comes to mind for me is to split the integrand into easier parts by long division.
 
  • #3
hello.world said:

Homework Statement


integrate (t^2) / (1+2t) . Wolfram alpha gave this as the answer: http://www4a.wolframalpha.com/Calculate/MSP/MSP957620di145hih25dggd00002hc5g230hb2h25hd?MSPStoreType=image/gif&s=24&w=229.&h=36. [Broken]

The Attempt at a Solution



I tried a u-substitution and couldn't arrive at a solution. Any other suggestions! Int by parts doesn't seem to work either!
The substitution u = 1+2t should work. I'm guessing that's what you tried, but you messed up somewhere along the way. Show your work.
 
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What is an integral?

An integral is a mathematical concept that represents the area under a curve. It is used to calculate the total accumulation of a quantity over a certain interval.

What is the difference between a definite and indefinite integral?

A definite integral has specific limits of integration, while an indefinite integral does not. Definite integrals give a numerical value, while indefinite integrals result in a function.

What are the different methods for evaluating integrals?

There are several methods for evaluating integrals, including the substitution method, integration by parts, and trigonometric substitution. In some cases, numerical methods such as the trapezoidal rule or Simpson's rule may also be used.

What is the fundamental theorem of calculus?

The fundamental theorem of calculus states that differentiation and integration are inverse operations. This means that the derivative of an integral is equal to the original function, and the integral of a derivative is equal to the original function.

How are integrals used in real-world applications?

Integrals are used in a variety of fields, such as physics, engineering, economics, and statistics. They can be used to calculate quantities such as velocity, acceleration, work, and probability. They also have applications in optimization problems and area/volume calculations.

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