How do I solve tricky integration questions for my upcoming exam?

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SUMMARY

This discussion focuses on solving complex integration problems in preparation for an integral exam. Key integration challenges include integrating functions such as ln^n(x), tan^n(x), and sec^(n) x. Participants suggest using differentiation techniques and substitution methods to tackle these problems. The conversation emphasizes the importance of understanding the relationship between differentiation and integration for solving these types of calculus questions.

PREREQUISITES
  • Understanding of basic calculus concepts, including integration and differentiation.
  • Familiarity with trigonometric functions and their properties.
  • Knowledge of substitution methods in integration.
  • Experience with logarithmic functions and their derivatives.
NEXT STEPS
  • Study integration techniques for logarithmic functions, specifically ln^n(x).
  • Learn how to integrate powers of trigonometric functions, particularly tan^n(x) and sec^(n) x.
  • Explore substitution methods in calculus to simplify complex integrals.
  • Practice problems involving the integration of rational functions, such as x/(a+bx)^(1/2).
USEFUL FOR

Students preparing for calculus exams, educators teaching integration techniques, and anyone seeking to improve their understanding of advanced integration methods.

avleen
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Hi, I am studying for my integral exam in 2 weeks,andim trying really hard to understand a few calc questions which i really can't get how to solve,
e.g
(ALL these questions are integrations questions)
1)ln^n(x)
i tried to put 1.ln^n (X) but i can't seem to get the answer right
^^^^ this is a derivation

2) same with tan^n (x)

i don't know how to integrate sec^(any even or odd power) x

x/(a+bx )1/2. how is this equal to 2/3b^2(bx-2a)(a+bx)^1/2
how do i derive tan^n(x)


Sinx/sin(x+alpha)

PLEASE help
 
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welcome to pf!

hi avleen! welcome to pf! :smile:

(have a square-root: √ and try using the X2 icon just above the Reply box :wink:)

let's start with tannx, = (tanx)n …

you need to use the https://www.physicsforums.com/library.php?do=view_item&itemid=353" …

you know how to differentiate xn, so to differentiate (tanx)n you put tanx = u …

ok, now you try it, and we'll see where you're going wrong :smile:​
avleen said:
x/(a+bx )1/2. how is this equal to 2/3b^2(bx-2a)(a+bx)^1/2


are you sure? that doesn't look right :redface:
 
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