How do you integrate #(tanx)^4 - Socratic
WEBOct 21, 2016 · The trick with this one is to split it up into two tan^2x terms and use some identities. int tan^4xdx = int tan^2xtan^2xdx = int tan^2x(sec^2x - 1)dx = int sec^2x(tanx)^2 - tan^2xdx = int (tanx)^2sec^2x - (sec^2x - 1)dx Now for the first half, you can use u-substitution (let u = tanx, du = sec^2xdx), and for the second half, intsec^2x = tanx.
Integrals of Trigonometric Functions - Calculus - Socratic
WEBSince the derivatives of \sin (x) and \cos (x) are cyclical, that is, the fourth derivative of each is again \sin (x) and \cos (x), it is easy to determine their integrals by logic. The integral and derivative of \tan (x) is more complicated, but can be determined by studying the derivative and integral of \ln (x).
How do you find the integral of tan^2 (x)sec(x) dx? - Socratic
WEBApr 25, 2015 · tan^3x /3 +C This can be easily be solved by using substitution. Let tan x =u, so that sec^2x dx=du int tan^2x sec x dx= intu^2du= u^3/3 +C=tan^3x /3 +C
How do you find the integral of tan^2(x) * sec^3(x) dx? - Socratic
WEBOct 23, 2015 · Alternative form for ∫secxdx. See the explanation section, below. Rewrite the integrand using tan^2x = sec^2x-1. Let's give the integral we want the name I I = int tan^2xsec^3x dx = int (sec^5x-sec^3x)dx Next we'll integrate sec^5x by parts. int sec^5x dx = int sec^3 x sec^2x dx Let u = sec^3 x and dv = sec^2x dx.
What is the Integral of tan^5(x) dx? - Socratic
WEBJun 30, 2016 · Explanation: The given is to find ∫tan5xdx. Solution: ∫tan5x ⋅ dx. ∫tan5x ⋅ dx = ∫tan3x ⋅ tan2xdx. ∫tan5x ⋅ dx = ∫tan3x ⋅ (sec2x −1)dx = ∫(tan3xsec2x −tan3x)dx. ∫tan5x ⋅ dx = ∫(tan3xsec2x)dx −∫tan3xdx. ∫tan5x ⋅ dx = ∫(tan3xsec2x)dx −∫tan2x ⋅ tanxdx. ∫tan5x ⋅ dx = ∫(tan3xsec2x)dx −∫ ...
What is the integral of int tan^3(x) dx? | Socratic
WEBJan 14, 2017 · For the first integral, apply the substitution u = tan(x) ⇒ du = sec2(x)dx, both of which are already in the integral. = ∫u.du − ∫tan(x)dx. = u2 2 − ∫tan(x)dx. = tan2(x) 2 −∫tan(x)dx. Now rewrite tan(x) as sin(x) cos(x) and apply the substitution v = cos(x) ⇒ dv = −sin(x)dx. = tan2(x) 2 −∫ sin(x) cos(x) dx. = tan2(x) 2 ...
What is the integral of #arctan(x)#? - Socratic
WEBAug 12, 2018 · What is the integral of #arctan(x)#? Calculus Introduction to Integration Integrals of Trigonometric ...
Show that the integral of tan(x) is ln|sec(x)| + C where C is a ...
WEBShow that the integral of tan (x) is ln|sec (x)| + C where C is a constant. First, recall that tan (x) can be rewritten in terms of sine and cosine. tan (x) = sin (x)/cos (x) The rephrasing of our question suggests that we should try the substitution rule of integration. We should substitute u=cos (x), since then du = -sin (x) dx and so sin (x ...
How do you integrate #tan^-1x/(1+x^2)#? - Socratic
WEBDec 24, 2016 · How do I evaluate the indefinite integral #int(tan^2(x)+tan^4(x))^2dx# ? How do I evaluate the indefinite integral #intx*sin(x)*tan(x)dx# ? See all questions in Integrals of Trigonometric Functions
What is #int tan^-1 x dx - Socratic
WEBFeb 20, 2018 · Explanation: We want to solve. I = ∫tan−1(x)dx. Use integration by parts / partial integration. ∫udv = uv − ∫vdu. Let u = tan−1(x) and dv = 1dx. Then du = 1 x2 + 1 dx and v = x. I = tan−1(x)x − ∫ x x2 +1 dx. Make a substitution u = x2 +1 ⇒ du dx = 2x.