calculus II
posted by Sarah
∫ tan^2 x sec^3 x dx
If the power of the secant n is odd, and the power of the tangent m is even, then the tangent is expressed as the secant using the identity
1 + tan^2 x = sec^2 x
I thought that since tan is even and sec is odd, we have to put this in terms of cosine and sine.
= ∫ (sin^2 x / cos^2 x) (1/ cos^3 x) dx
= ∫ sin^2 x / cos^5 x dx
u = sin x
du= cos dx
= ∫ sin^2 x cos^5 x dx
=∫ u^2 cos^5 x (du/cos x)
= ∫ u^2 / (1  u^2)^3 du
then split this into two integrals, but how do you do this? Thank you

Sarah
please for any help. I'm just really confused with this problem.
Respond to this Question
Similar Questions

geometry 1
a secantsecant angle intercepts arcs that are 3/5 and 3/8 respectively. Find the measure of the secantsecant angle. 
calculus (check my work please)
Not sure if it is right, I have check with the answer in the book and a few integral calculators but they seem to get a different answer ∫ sec^3(x)tan^3(x) dx ∫ sec^3(x)tan(x)(sec^2(x)1) dx ∫ tan(x)sec(x)[sec^4(x)sec^2(x)] … 
Trig Functions
Which of the following lists contains only functions with vertical asymptotes in their graphs? 
Calculus AP
I'm doing trigonometric integrals i wanted to know im doing step is my answer right? 
mathIV
HOW TO PROVE TANGENT THETA +(SECANT THETA1 DIVIDE TANGENT THETASECANT THETA+1=TANGENT THETA+SECANT THETA 
Calculus
Graph the function f(x)=x+4/x Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8] c= Notice that if … 
Geometry
A secant and a tangent to a circle intersect in a 42 degree angle. The two arcs of the circle intercepted by the secant and tangent have measures in a 7:3 ratio. Find the measure of the third arc. If someone could help me figure out … 
Math
Consider the graph of the parabola f(x)equals=x squaredx2. For xgreater than>0 and hgreater than>0, the secant line through (x,f(x)) and (xplus+h,f(x+h)) always has a greater slope than the … 
Math (Calculus) (mean value theorem emergency)
Consider the graph of the function f(x)=x^2x12 a) Find the equation of the secant line joining the points (2,6) and (4,0). I got the equation of the secant line to be y=x4 b) Use the Mean Value Theorem to determine a point c in … 
Geometry
If a tangent segment and a secant segment are drawn to a circle from the same point, the external part of the secant segment is longer than the tangent segment. True or False?