We are asked in the problem to evaluate the integral of <span>(cosec^2 x-2005)÷cos^2005 x dx. The function is an example of a complex function with a degree that is greater than one and that uses special rules to integrate the function via the trigonometric functions. For example, we integrate
2005/cos^2005x dx which is equal to 2005 sec^2005 x since sec is the inverse of cos. The integral of this function when n >3 is equal to I=</span><span>∫<span>sec(n−2)</span>xdx+∫tanx<span>sec(n−3)</span>x(secxtanx)dx
Then,
</span><span>∫tanx<span>sec(<span>n−3)</span></span>x(secxtanx)dx=<span><span>tanx<span>sec(<span>n−2)</span></span>x/(</span><span>n−2)</span></span>−<span>1/(<span>n−2)I
we can then integrate the function by substituting n by 3.
On the first term csc^2 2005x / cos^2005 x we can use the trigonometric identity csc^2 x = 1 + cot^2 x to simplify the terms</span></span></span>
Answer:
1
Step-by-step explanation:
First one: divide multiply 2(1x) which would equal 2x then do 2*3 then u would subtract 5 which should get you to the simplified form 2x+1
Second one: do 3(1x) which would equal 3x then do 7*3 which would equal 21 than do plus 3x which should get you to the simplified form of 6x+21
Third one: Do 4(1x) which equals 4x than do 4*2 which equals 8 than plus eight which should get you to the simplest form of 4x+16
Fourth one: do 4(1x) which would equal 4x then do 4*1 which equals 4 than subtract 6 which should get you to the simplest form of 4x-2
Fifth one: do 2(3x) which equals 6x then do 2*2 which equals 4 than subtract 5x which should get you to the simplest form of x+4
Sixth one: do 5(1x) which equals 5x than do 5*-4 which equals -20 than add 10 which gets you to the simplest form of 5x-10
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Answer:
Step-by-step explanation:
Solve the following equation:
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-In order to solve a pair of equations by using substitution, you first need to solve one of the equations for one of variables and then you would substitute the result for that variable in the other equation:
-First equation:
-Second equation:
-Choose one of the two following equations, which I choose the first one, then you solve for 
by isolating
-Subtract 
to both sides:
-Subtract 
to both sides:
-Divide both sides by 
:
-Multiply 
by 
:
-Substitute 
for in the second equation, which is :
Multiply by 
:
-Combine like terms:
-Subtract 
to both sides:
-Multiply both sides by 
:
-After you have the value of 
, substitute for 
onto this equation, which is :
-Multiply 
and 
:
-Since both and 
have the same denominator, then add the numerators together. Also, after you have added both numerators together, reduce the fraction to the lowest term:
