2016年5月10日 · color(red)(int sec^3 x*dx=1/2*sec x*tan x+1/2*ln(sec x+tan x)+C) This is done using Integration by Parts int u*dv=uv-int v*du Let u=sec x Let dv=sec^2 x*dx Let v=tan ...

2014年7月25日 · Answer is y' = 3* sec^2x*secx*tanx The solution is, For problems like these, y=f(x)^n then y' = n*f(x)^(n-1)*f'(x) (this is the Power Chain Rule) Similarly for the question asked above y' = 3* sec^2x*secx*tanx

2014年8月6日 · sec x is equal to 1/cosx. Thus, sec^3 x is an equivalent statement to 1/(cosx)^3. And, we know that this is equivalent to (cos x)^(-3). So, all we need to do is use the power rule, keeping in mind to use the chain rule on cos x: dy/dx = -3*(cos x)^(-4) * d/dx[cos x] = -3*(cos x)^(-4) * (-sinx) = 3sinx(cos x)^(-4) = (3sinx)/(cos^4 x)

2016年10月4日 · sec^3x/3+C When working with integrals of secant and tangent, it's important to remember the following: d/dxtanx=sec^2x d/dxsecx=secxtanx Here, we see that we can write sec^3x(tanx) as sec^2x(secxtanx), which is perfect, since it composed of sec^2x and the derivative of secant, secxtanx. This indicates to us that we want to use a substitution of …

2018年5月22日 · 1. Integrating by parts. Since #sec^3(x) = sec^2(x) sec(x)#,. #int sec^3(x)dx = int sec^2(x) sec(x)dx# With #u=sec(x) <=> u'=sec(x)tan(x)#, #v'=sec^2(x) <=> v=tan(x ...

2015年10月23日 · 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. Then du = 3tanx sec^3x dx and v = tanx We get int sec^5 x dx = sec^3x …

\"使用Cymath數學問題求解器獲得sec(x)^3的積分的答案

\[\int \sec^{3}x \, dx\] +. > < ...

2017年5月15日 · To differentiate, use the chain rule: Given: y= (sec(3x))^2 y'=2[sec(3x)][sec(3x)tan(3x)](3) y'= 6 sec^2 (3x) tan(3x)

\"使用Cymath数学问题求解器获得sec(x)^3的积分的答案