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Nope
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Homework Statement
[tex]\int(2x^2+1)^7[/tex]
Homework Equations
The Attempt at a Solution
u=2x^2+1
du=4xdx
u7 (1/4x)du
I am stuck... I don't know what to do next...
Try to remember to put in the differential...Nope said:Homework Statement
[tex]\int(2x^2+1)^7[/tex]
Substitution won't work in this case, which you already found out. If you expand [itex]\int(2x^2+1)^7[/itex], you'll get a polynomial that you can integrate pretty easily.Nope said:Homework Equations
The Attempt at a Solution
u=2x^2+1
du=4xdx
u7 (1/4x)du
I am stuck... I don't know what to do next...
Nope said:wow, so i have to expand everything out? (2x^2+1)^7
that's a lot
is there any other way to do it?
An antiderivative is the inverse operation of a derivative. It is a function that, when differentiated, gives the original function.
To find the antiderivative of a function, you can use the reverse power rule, which states that the antiderivative of a polynomial is the polynomial with each term raised to the next higher power, divided by the new power.
Yes, the constant of integration, denoted as "+ C", is always included when finding an antiderivative. This is because when differentiating, the constant will become 0, so it is important to include it in the antiderivative.
The derivative and antiderivative are inverse operations of each other. This means that the derivative of a function gives the slope of the tangent line at any given point, while the antiderivative gives the original function when differentiated.
Yes, there are some common antiderivatives that you can memorize to make the process quicker. These include the antiderivatives of polynomial functions, exponential functions, and trigonometric functions, among others.