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sora4ever1
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i have this question can anyone help me please thx.
what is the indefinate integral of tan^7xsec^4x goodluck.
what is the indefinate integral of tan^7xsec^4x goodluck.
TD said:What have you tried so far?
bomba923 said:Basically, I believe you must simply save a factor of [tex] \sec ^ 2 x[/tex]
and use [tex]\sec ^ 2 x = 1 + \tan ^ 2 x [/tex] to express the remaining factors
in terms of [itex] \tan x [/itex]. Next, simply substitute with respect to [tex] \tan x [/tex].
(I think it's called "u"-substitution in some texts).?
As you should already know, :shy:
[tex] \frac{d}{dx} \tan x = \sec ^ 2 x [/tex]
*Here's that method, put in action :
[tex] \int {\tan ^7 x\sec ^4 x\,dx} = \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\sec ^2 x\,dx} = [/tex]
[tex] \int {\tan ^7 x\left( {1 + \tan ^2 x} \right)\,d\left( {\tan x} \right)} = \boxed{\frac{{\tan ^8 x}}{8} + \frac{{\tan ^{10} x}}{{10}} + C} [/tex]
!It is very likely that somewhere I made an error!...
Somewhere...some silly error
No, this is correctbomba923 said:!It is very likely that somewhere I made an error!...
Somewhere...some silly error
The indefinite integral, also known as the antiderivative, is a mathematical concept used in calculus to find the original function from its derivative. It represents a family of functions that differ only by a constant.
The indefinite integral does not have any upper or lower limits, while the definite integral has specific limits of integration. The indefinite integral also includes a constant of integration, whereas the definite integral results in a single number.
The process for finding the indefinite integral involves using integration techniques, such as u-substitution or integration by parts, to manipulate the derivative back into its original function form. It is also important to include the constant of integration in the final answer.
The indefinite integral is used in various fields, such as physics, engineering, and economics, to solve problems involving rates of change. For example, it can be used to find the position of an object given its velocity, or the total cost of production given the marginal cost function.
The notation used for the indefinite integral is ∫ f(x) dx, where f(x) is the original function and dx represents the variable of integration. The indefinite integral is often written as F(x) + C, where C is the constant of integration.