2016年6月30日 · What is the Integral of tan5(x)dx? ∫tan5xdx = 1 4tan4x − 1 2 ⋅ tan2x +lnsecx + C. The given is to find ∫tan5xdx. Solution: ∫tan5x ⋅ dx = ∫tan3x ⋅ tan2xdx. ∫tan5x ⋅ dx = ∫tan3x ⋅ (sec2x −1)dx = ∫(tan3xsec2x −tan3x)dx. ∫tan5x ⋅ dx = ∫(tan3xsec2x)dx −∫tan3xdx. ∫tan5x ⋅ dx = ∫(tan3xsec2x)dx −∫tan2x ⋅ tanxdx.

2014年10月18日 · There is an easy way to evaluate $\int \sin^n(x)\cos^m(x)\,dx$ when at least one of $n,m$ is odd. Say $n$ is odd. Then keep one factor of $\sin$ and convert all the rest to $\cos$ , and substitute $u=\cos x, du=-\sin x\,dx$ .

Differentiate using the Power Rule which states that is where .. Step 1.1.4. Multiply by .

Here's my attempt at the problem: $\int{\tan^{5}(x)\sec^4(x)}dx= \int{\frac{\sin^5(x)}{\cos^9(x)}}\,dx= \int{\frac{\sin(x)(\sin^2(x))^2}{\cos^9(x)}}\,dx= \int{\frac{\sin(x)(1-\cos^2(x))^2}{\cos^9(...

2017年1月13日 · How do you evaluate the integral ∫tan5 x? ∫tan5xdx = 1 4tan4x − 1 2tan2x − ln|cosx|+ C. Using the trigonometric identity: tan2x = sec2x −1. we can observe that in general. ∫tannxdx = ∫(sec2x − 1)tann−2xdx = ∫tann−2xsec2xdx − ∫tann−2xdx. Remembering that: d dx tanx = sec2x. the first integral is easy to solve:

$$=\displaystyle \int (tan^3xsec^2x - tanx(sec^2x-1))dx$$ $$=\displaystyle \int (tan^3xsec^2x - tanxsec^2x + tanx)dx$$ $$=\dfrac{tan^4x}{4} - \dfrac{tan^2x}{2} + ln|secx| + C$$

2015年11月2日 · # =int ((cosx)^-5 -2(cosx)^-3 +(cosx)^-1) sinx dx# Now integrate by substitution with #u = cosx# Alternatively, one could use the reduction formula for #int tan^nx dx# .

2015年4月8日 · 2014-01-24 求(tanx)^5的不定积分！ 要过程！绝对给分 1 2013-01-04 求(tanx)^5的不定积分 18 2010-11-20 (tanx)的n次方的不定积分的递推公式怎么求？ 62 2012-06-12 不定积分∫tan^4xdx 344 2015-06-03 1/sinx的3次方的不定积分怎么算，求过程 148 2014-12-28 求tanX的四次方的不定积分，用什么换元积分法。

2020年3月13日 · Suppose I = ∫tan 5 x dx. The equation can be written as. I = ∫tan 2 x tan 3 x dx. On using standard formula . I = ∫(sec 2 x - 1)tan 3 x dx. On splitting the equation . Putting the value of t, we get

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