- #1
413
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can anybody help me with this problem
Evaluate :
integral 3x (sinx/cos^4x) dx
Evaluate :
integral 3x (sinx/cos^4x) dx
In summary, The conversation is about evaluating the integral 3x (sinx/cos^4x) dx, which can be rewritten as 3\int x\tan x\sec^{3} x using integration by parts. The variables u, dv, v, and du are discussed and it is determined that u = x and dv = \tan x \sec^{3} x, with integration by parts needed for dv to find v. A small correction is made to the equation suggested by another person.
- #2
courtrigrad
- 1,236
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Is it [tex] \int \frac{3x\sin x}{\cos^{4} x} [/tex]?
Rewrite it as [tex] 3\int x\tan x\ sec^{3} x [/tex] and use integration by parts
Rewrite it as [tex] 3\int x\tan x\ sec^{3} x [/tex] and use integration by parts
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- #3
413
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i know the equation for intergration by parts is
intergral u dv = uv -intergral v du
can u tell me which variable is which?...u, du, v, dv=?...there seems to have 3 different variable.
intergral u dv = uv -intergral v du
can u tell me which variable is which?...u, du, v, dv=?...there seems to have 3 different variable.
- #4
courtrigrad
- 1,236
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Let [tex] u = x [/tex] and [tex] dv = \ tan x \sec^{3} x [/tex]. You will then need to use integration by parts on [tex] dv [/tex] to get [tex] v [/tex].
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- #5
HallsofIvy
Science Advisor
Homework Helper
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I'm sure courtrigrad meant [itex]u= x[/itex] and [itex]dv= tan x sec^3 xdx[/itex] (with out the "x" in dv).
- #6
courtrigrad
- 1,236
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yep, thanks catching that 
FAQ: What is the Integral of 3x (sinx/cos^4x) dx?
What is the integral of 3x (sinx/cos^4x) dx?
The integral of 3x (sinx/cos^4x) dx is equal to (-3/5)cos^5x + C.
How do you solve an integral with trigonometric functions?
To solve an integral with trigonometric functions, you can use trigonometric identities, integration by parts, or substitution. In this case, the integral can be solved using substitution.
What is the domain of the function 3x (sinx/cos^4x)?
The domain of the function 3x (sinx/cos^4x) is all real numbers except for values of x where cos^4x = 0. This means that the domain is all real numbers except for values of x that are multiples of pi/2.
Can this integral be solved using the power rule?
No, this integral cannot be solved using the power rule because the power rule only applies to integrals of the form x^n, where n is a constant. In this case, the exponent is not a constant but a function of x.
Can this integral be solved using a calculator?
Yes, this integral can be solved using a calculator by entering the function into the calculator and using the integral function or by using the calculator's graphing feature to find the area under the curve.