# How to solve: Evaluate the integral of tan^7(x/2) sec^2(x/2) dx. By signing up, you'll get thousands of step-by-step solutions to your homework

Solve the integral = - ln |u| + C substitute back u=cos x = - ln |cos x| + C Q.E.D. 2. Alternate Form of Result. tan x dx = - ln |cos x| + C = ln | (cos x)-1 | + C = ln |sec x| + C

sec(x) dx. ln(sec(x)+tan(x)). int. csc(x)  Integrate : ∫√sinxcos92xdx. views.

Tap for more steps Rewrite as . Rewrite as . Rewrite in terms of sines and cosines. 2015-02-19 · How do you prove the integral formula #intdx/(sqrt(x^2+a^2)) = ln(x+sqrt(x^2+a^2))+ C# ? See all questions in Integration by Trigonometric Substitution Impact of this question 2009-03-02 · For the best answers, search on this site https://shorturl.im/avdZf.

Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. Tangens (tan, ibland tg) är en trigonometrisk funktion och definieras som [1] tan ⁡ α = sin ⁡ α cos ⁡ α {\displaystyle \tan \alpha ={\frac {\sin \alpha }{\cos \alpha }}} Alternativt kan tangens definieras med hjälp av en rätvinklig triangel Integration von tan(x)² im Mathe-Forum für Schüler und Studenten Antworten nach dem Prinzip Hilfe zur Selbsthilfe Jetzt Deine Frage im Forum stellen! Evaluate integral of 1/(tan(x)^2) with respect to x.

## Figure 1: Graphs of 2tan2 x (blue) and sec x (red). In fact, that is the case: sin2 x tan2 x = cos2 x 1 2− cos x = cos2 x = sec 2 x − 1 1 2 1 2 1 We conclude that tan x = sec and so the two results are equiva­ 2 2 x − 2 lent up to an added constant. Both answers are correct. 2

2. Alternate Form of Result. tan x dx = - ln |cos x| + C = ln | (cos x)-1 | + C = ln |sec x| + C For a definite integral, one must figure out how the bounds of integration change.

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I=∫π80[sec2(2x)−1]dx=[tan2x2−x]π80 =[tanπ 42−π8−tan02+0]=12−π8=4−π8.

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