Efficiently Solve ∫tan^3(x) dx Using tan^2(x)+1=sec^2(x) in 3 Steps

  • Thread starter Thread starter november1992
  • Start date Start date
  • Tags Tags
    Integral
november1992
Messages
120
Reaction score
0

Homework Statement



∫tan^{3}x dx

Homework Equations



tan^{2}x+1 = sec^{2}x

tan^{3}x = tan^{2}x * tan(x)

The Attempt at a Solution



∫tan^{2}x * tan(x) dx

∫(sec^{2}x -1 ) tan(x) dx

∫(sec^{2}xtan(x) -∫tan(x)

∫u du - sec^{2}x

u^{2}/2 - sec^{2}x

tan^{2}x/2 - sec^{2}x
 
Physics news on Phys.org
Oh damn. I just realized integral of tanx is ln|secx|.

I got it wrong on my test :(
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

How to Integrate [1/(x^2 + 3)] dx?
Replies
5
Views
3K
Solve the given first order differential equation
Replies
8
Views
2K
Trouble seeing the difference between autograder answer and my own
Replies
2
Views
1K
Integrate [cosec(30°+x)-cosec(60°+x)] dx in terms of tan x
Replies
3
Views
1K
Solve this problem that involves implicit differentiation
Replies
15
Views
2K
lim x-->0 ##\frac{x tan2x -2xtanx} {(1-cos2x)^2}##
Replies
5
Views
1K
Differentiate ##f(x)=x\cos{x}+2\tan{x}: D/dx ##\tiny{2.4.2}##
Replies
10
Views
1K
Can you handle this integration with limits problem?
Replies
3
Views
2K
How Do You Integrate tan²x sec^4x dx?
Replies
2
Views
3K
Calculus ## G(y, z)=z\frac{\partial}{\partial z}F(y, z)-F(y, z) ##?
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top