Integral of sec 5x

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August undefined, 2024

Nettet11. feb. 2016 · Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer sente Feb 11, 2016 ∫sec2(5x)dx = 1 5tan(5x) + C Explanation: Noting that d dx tan(x) = sec2(x) Let u = 5x ⇒ du = 5dx ⇒ dx = 1 5du ∫sec2(5x)dx = ∫ sec2(u) 5 du = 1 5 ∫sec2(u)du = 1 5 tan(u) + C = 1 5 tan(5x) +C Answer link Nettet10. nov. 2024 · After completing the integral, I ended up with $\int\sec^5x dx= \frac{\tan^3x\sec x}4+\frac{3\tan x\sec x}8+\frac{3\ln(\tan x+\sec x)}8+C$ Which is very …

How do you find the integral of int sec^2(5x)dx? Socratic

Nettet18. okt. 2024 · To convert this integral to integrals of the form ∫cosjxsinxdx, rewrite sin3x = sin2xsinx and make the substitution sin2x = 1 − cos2x. Thus, ∫cos2xsin3xdx = ∫cos2x(1 − cos2x)sinxdx Let u = cosx; then du = − sinxdx. = − ∫u2(1 − u2)du = ∫(u4 − u2)du = 1 5u5 − 1 3u3 + C = 1 5cos5x − 1 3cos3x + C. Exercise 7.2.2 Evaluate ∫cos3xsin2xdx. Hint … NettetAnswer (1 of 2): I=sec^5 x cosec^3 x =1/{sin^3 x cos^5 x} Numerator and denominator devide by cos^8 x =(sec^8 x)/(tan^3 x) =(sec^6 x × sec^2 x )/(tan^3 x) =[(sec^2 x)^3 sec^2 x ]/(tan^3 x) I=[(1+tan^2 x)^3 sec^2 x]/(tan^3 x)…(1) Put tanx=t Diff w.r.t.x sec^2 x dx = dt From (1) I=(1+t^2... qyhyyy

Evaluate the integral \int \sec^5 x \tan x\, dx

NettetCalculus Evaluate the Integral integral of tan (x)^5sec (x)^7 with respect to x ∫tan 5(x)sec 7(x)dx Factor out tan4(x). ∫tan4(x)tan(x)sec7(x)dx Simplify with factoring out. Tap for more steps... ∫(tan2(x))2tan(x)sec7(x)dx Using the Pythagorean Identity, rewrite tan2(x) as - 1 + sec2(x). ∫( - 1 + sec2(x))2tan(x)sec7(x)dx Let u = sec(x). Nettet8. okt. 2024 · In this video we have integrated sec^5x. Here to make the integral short, we have used the integration of sec^3x. This integration has already been done in our … Nettet13. mar. 2024 · answered Mar 13, 2024 by Prerna01 (52.4k points) selected Mar 13, 2024 by RahulYadav. Best answer. Suppose I = ∫tan5x sec4x dx. The equation can be written as. Suppose tan x = t, now. sec2x dx = dt. On substituting the value of x. ← Prev Question Next Question →. qxl lukker

Integral of sec 5x

Formulas - Find the integral int(xsin(5x))dx SnapXam

NettetA: We have to find the integral of the given expression The expression is ∫tan5xsec8 (x)dx Q: Evaluate the indefinite integral. (Use C for the constant of integration.) x (x? + 8)10 dx A: Click to see the answer Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx 3 + cos? X A: Indefinite integral is below NettetWe can solve the integral \int x\sin\left(5x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv …

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NettetThe integral now appears on both sides of the equation and we can solve for it obtaining a reduction formula: ∫sec 5sdx= 41(tanxsec 3+3∫sec 3xdx) Solve now the resulting integrals with the same procedure: ∫sec 3xdx=tanxsecx−∫tanxd(secx) ∫sec 3xdx=tanxsecx−∫tan 2xsecxdx ∫sec 3sdx=tanxsecx−∫(sec 2x−1)secxdx ∫sec 3sdx=tanxsecx+∫secxdx−∫sec … NettetWe integrate sec 5x using two methods. Differentiating verifies the answers. Also, the integral will be evaluated between two values of x to give the area under a portion of …

NettetSince 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). NettetEvaluate the integral ∫ sec5xtanxdx ∫ sec 5 x tan x d x Secant and Tangent: Recall the relationship between secant and tangent. The Pythagorean identity that relates the two is tan2θ+1= sec2θ....

NettetCalculus Evaluate the Integral integral of sec (5x)tan (5x) with respect to x ∫ sec (5x)tan (5x) dx ∫ sec ( 5 x) tan ( 5 x) d x Let u2 = sec(5x) u 2 = sec ( 5 x). Then du2 = 5sec(5x)tan(5x)dx d u 2 = 5 sec ( 5 x) tan ( 5 x) d x, so 1 5du2 = sec(5x)tan(5x)dx 1 5 d u 2 = sec ( 5 x) tan ( 5 x) d x. Rewrite using u2 u 2 and d d u2 u 2. NettetDerivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin …

NettetLet I = ∫ sec 4 x d x = ... Integration by Substitution Method - Problem 3. 10 mins. Integration by Substitution Method - Problem 4. 17 mins. Integration of the form f(p)p'(x) 6 mins. Shortcuts & Tips . Problem solving tips > Memorization tricks > Mindmap >

Nettet21. des. 2024 · The power of the sine term is odd, so we rewrite sin5x as sin5x = sin4xsinx = (sin2x)2sinx = (1 − cos2x)2sinx. Our integral is now ∫ (1 − cos2x)2cos8xsinx dx. Let u = cosx, hence du = − sinx dx. Making the substitution and expanding the integrand gives qyasuka twitterNettetWe can solve the integral \int x\sin\left(5x\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. qyianna s12NettetThe easiest way is to remember that the derivative of sec t is sec t tan t . If you happen not to remember that, one useful strategy is to convert to sines and cosines. So we are interested in. ∫ sin ( 7 x) cos 2 ( 7 x) d x. Let u = cos ( 7 x). Then d u = − 7 sin ( 7 x) d x, so we want. ∫ − 1 7 ⋅ 1 u 2 d u. Share. Cite. qxyzhai.oneNettet7. integral 4 sin 5x sin x dx integral cos 3x cos x dx integral 3 sin 2x dx = integral 2 (sin6x+cos4x) dx , integral 1/2(cos4x +cos 2x) dx, 3 integral sin2x dx 8. 1. ... qyld net asset valueNettetFree math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. qymaen jai sheehalNettetIntegrate : ∫sec 5xtanxdx A 4tan 5x+C B 51tan 5x+C C 5log∣cosx∣+C D none of these Medium Solution Verified by Toppr Correct option is D) Was this answer helpful? 0 0 Similar questions Solve: ∫e xsecx(1+tanx)dx equals Medium View solution > Evaluate : ∫e xsecx(1+tanx)dx Medium View solution > View more Get the Free Answr app qylinkNettet7. integral 4 sin 5x sin x dx integral cos 3x cos x dx integral 3 sin 2x dx = integral 2 (sin6x+cos4x) dx , integral 1/2(cos4x +cos 2x) dx, 3 integral sin2x dx 8. 1. ... Berapakah hasil dari: 1. Integral tan (4x-2) sec dx 2. Integral (tan²x+4) dx 3. Integral (sin x-cos x)² dx Bantu ya . Integral. ∫(tan² x + 4) dx = ∫(sec² x - 1 + 4) dx qyleen jomarr salting