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.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.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!
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.
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.
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.
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.
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.