Since you did not specify any limits of integration, I assume you are looking for the indefinite integral of this expression:
tan2(x)cos5(x)
with respect to x (dx). Using the following identity:
tan(x) = sin(x) / cos(x)
The original expression can be rewritten as:
(sin2(x) / cos2(x))cos5(x)
Which further simplifies to:
sin2(x)cos3(x)
Which can be expanded to:
sin2(x)cos2(x)cos(x)
Using the identity:
sin2(x) + cos2(x) = 1
which implies:
cos2(x) = 1 - sin2(x)
which makes the expression from above able to be simplified into:
sin2(x)(1 - sin2(x))cos(x)
From here, you can use u-substitution by using the substitution:
u = sin(x)
du = cos(x) dx => dx = du/cos(x)
So after u substitution:
int(sin2(x)(1 - sin2(x))cos(x)) dx
becomes:
int(u2(1-u2)) du
int(u2-u4) du
From here, elementary antiderivatives can be used:
anti(u2) = (1/3)(u3)
anti(u4) = (1/5)(u5)
which yields a final indefinite integral in u of:
(1/3)u3-(1/5)u5 + C
where C is the constant of integration (since this is an indefinite integral).
Back-substituting with the u-substitution from before (u=sin(x)), the final indefinite integral in x is:
(1/3)sin3(x) - (1/5)sin5(x) + C
There is no such thing as 1 SQUARED by 5. It is actually 1 to the 5th power, which is 1.
The answer depends on what the question is!
C squared times the square root of 5cd over 2 times d to the third power
a quantity multiplied by itself
It is the 15th power.
There is no such thing as 1 SQUARED by 5. It is actually 1 to the 5th power, which is 1.
x to the 5th power times y to the fourth power
6x to the 5th power (im pretty sure)
The answer depends on what the question is!
Any prime number to the 5th power squared has 11 factors, like 1024 or 59049.
jhuhuhu
C squared times the square root of 5cd over 2 times d to the third power
It is: 5*5 = 25
My iTouch calculator isn't working, so I will simplify the problem for you: x to the 5th power = -4
a quantity multiplied by itself
7 to the 5th power is 16807.
: x squared times square root of x : : = x^2 * x^(1/2) : = x^[2+(1/2)] : = x^[(4/2)+(1/2)] : = x^(5/2) : which is the same thing as : square root of (x raised to the 5th power)