Can substitution help solve this antiderivative problem?

Thread starter redfilth
Start date Jul 11, 2011
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Antiderivatives

In summary, an antiderivative is the inverse operation of a derivative, and can be found by reversing the steps of differentiation using various rules. The notation used for antiderivatives is the integral symbol, and there is a difference between definite and indefinite antiderivatives in terms of specific limits of integration. Additionally, the antiderivative of a function can be used to find the area under the curve of that function.

Jul 11, 2011

redfilth

Problem:
[tex](x^2+2x)/sqrt[x^3+3x^2+1][/tex]

[tex]= 2/3/sqrt[(x+3x)^2+1] [/tex] is this the answer?

i don't knw how to solve it stepbystep..
can someone show me pls?

Last edited by a moderator: Jul 11, 2011

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Jul 11, 2011

lanedance

Homework Helper

hi redfilth

this could be a good candidate for substitution - can you think of a good one to try?

What is an antiderivative?

An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, gives the original function.

What is the process for finding an antiderivative?

The process for finding an antiderivative involves reversing the steps of differentiation. This includes using the power rule, product rule, quotient rule, and chain rule in reverse.

What is the notation used for antiderivatives?

The notation used for antiderivatives is the integral symbol (∫), which represents the process of finding an antiderivative. The function to be integrated is written after the integral symbol, followed by the variable of integration.

What is the difference between a definite and indefinite antiderivative?

A definite antiderivative has specific limits of integration, while an indefinite antiderivative does not. This means that a definite antiderivative will result in a numerical value, while an indefinite antiderivative will result in a function.

What is the relationship between antiderivatives and the area under a curve?

The antiderivative of a function can be used to find the area under the curve of that function. This is because the definite integral of a function is equal to the difference between its antiderivative evaluated at the upper and lower limits of integration.