Tan^2 Integrals

I'm having a hard time understanding how to do Integrals involving tan^2. I have two problems:
1. Find the integral of (tan^2 y +1)dy
2. Find the integral of (7tan^2 u +15)du

1. My approach to it is to replace the tan^2 y portion of the problem with sec^2 y -1, but it doesn't give me the answer that was given once I've worked it out. Can someone explain to me what I'm doing wrong and how I need to approach these problems?
2. For the latter question, I have no idea how they got the solution 7tanu +8u+C. None as far as tan is concerned and even less of an idea of how they got 8u.

  1. 👍 0
  2. 👎 0
  3. 👁 243
  1. don't forget your trig identities
    tan^2+1 = sec^2
    ∫sec^2 y dy
    is easy, right?

    7tan^2 u + 15 = 7tan^2 u+7 + 8
    = 7sec^2 u + 8
    Now we're back to
    ∫7sec^2 u + 8 du

    1. 👍 0
    2. 👎 0
  2. Thank you very much for your help Steve. I see now where I was going wrong with the problems and feel slightly embarrassed. Thanks again! :)

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Pre-calculus help

    I have two problems I am stuck on, if you could show me how to solve the problems it would be much appreciated. 1) Find sin 2x, cos 2x, and tan 2x from the given information. tan x = − 1/6, cos x > 0 sin 2x = cos 2x = tan 2x =

  2. calculus

    If limit as delta x approaches 0 of tan(0+Δx)-tan(0)/Δx =1 which of the following is false: d/dx [tanx]=1 the slope of y = tan(x) at x = 0 is 1 y = tan(x) is continuous at x = 0 y = tan(x) is differentiable at x = 0

  3. math

    i’m having a hard time understanding this. “write an inequality to represent the situation. the temperature stays above -15”

  4. Math

    solve for r There is a right triangle with the hypotenuse as r , the angle as 45 degrees and opposite side as 20. I am having a hard time finding this out. I had tan 45 = 1.61 20(1.61) = 32.4 but this is wrong.

  1. Math-Trigonometry

    Show that if A, B, and C are the angles of an acute triangle, then tan A + tan B + tan C = tan A tan B tan C. I tried drawing perpendiculars and stuff but it doesn't seem to work? For me, the trig identities don't seem to plug in

  2. Trigonometry

    Hello, everyone: I am working on finding the exact values of angles that are less common and are therefor not found easily on the Unit Circle (at least, they are not labeled). For example, the problem I am asking about is: 10)

  3. End behavior models

    Thanks for the help with my previous problems Roger & Leo. It was really helpful. Now I want to know how to find the right and left end behavior models and horizontal tangents for the inverse functions, say y = tan inverse(x) I

  4. Calculus AP

    I'm doing trigonometric integrals i wanted to know im doing step is my answer right? ∫ tan^3 (2x) sec^5(2x) dx =∫ tan^2(2x) sec^4(2x) tan*sec(2x) dx =∫ (sec^2(2x)-1)sec^4 tan*sec(2x) dx let u=sec x, du= 1/2 tan*sec(2x) dx

  1. Trig

    h t t p : / / m a t h c e n t r a l . u r e g i n a . c a / Q Q / d a t a b a s e / Q Q . 0 9 . 9 9 / a n g e l a 2 . 2 . g i f give that picture how do I solve for (h) I know that you you From the diagram tan(3.5) = h/(13 + x)

  2. Pre-Algebra

    5h – 9 = –16 + 6h Answer Choices: 4 –7 7 10 I need a step-by-step response cause I'm having a hard time understanding.

  3. Calculus

    Write 2.445353535353... as a fraction I'm learning integrals right now and this is part of the exercises under it. Is there a trick to this? Using integrals? Thank you very much!

  4. calculus/finite

    I am taking an online finite math class, so I don't have an instuctor to sit down with me and help me. The text book is so hard to follow. One of the problems I have having a hard time with gives an initial tableau and asks us to

You can view more similar questions or ask a new question.