2014年12月19日 · See explanation. This will be a long answer. So what you want to find is: int cos^6(x)dx There's a rule of thumb that you can remember: whenever you need to integrate an even power of the cosine function, you need to use the identity: cos^2(x) = (1+cos(2x))/2 First we split up the cosines: int cos^2(x)*cos^2(x)*cos^2(x) dx Now we can replace every cos^2(x) with the identity above: int (1+cos ...

2018年1月18日 · I don't think that #cos(x^6)# has an antiderivative expressible with elementary functions, so I assume you want to find #int\ cos^6(x)\ dx#. First, recall that #cos(2theta)=2cos^2(theta)-1# , or #cos^2(theta)=(1+cos(2theta))/2# .

2017年2月18日 · #int cos^6xdx = sinxcos^5x + 5 int cos^4x - 5int cos^6x dx# As the integral is on both sides we can solve for it: #6 int cos^6xdx = sinxcos^5x + 5 int cos^4xdx #

The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions.

2018年7月29日 · int cos^6x dx = ( 8cos^5x sinx +10 cos^3x sinx +15cosxsinx+15x)/48+C Write the integrand as: cos^6x = cos^5x * cosx So: int cos^6x dx = int cos^5x * cosx dx Integrate by parts: int cos^6x dx = int cos^5x d/dx (sinx) dx int cos^6x dx = cos^5x sinx - int sinx d/dx (cos^5x) dx int cos^6x dx = cos^5x sinx + 5 int sin^2x cos^4x dx Use now the identity: sin^2x = 1-cos^2x int cos^6x dx = cos^5x sinx ...

"The fundamental trigonometric identities" are the basic identities: •The reciprocal identities •The pythagorean identities

2018年3月9日 · We want to expand . #sin^6(x)# One way is to use these identities repeatedly . #sin^2(x)=1/2(1-cos(2x))# #cos^2(x)=1/2(1+cos(2x))#

2018年3月9日 · We'll use rarra^3+b^3=(a+b)(a^2-ab+b^2) rarra^2+b^2=(a-b)^2+2ab rarrsin^2x+cos^2x=1 rarr2cos^2x=1+cos2x and rarr2sin^2x=1-cos2x LHS=cos^6(x)+sin^6(x) =(cos^2x)^3+(sin ...

2018年3月21日 · How do I evaluate the indefinite integral #intsin^6(x)*cos^3(x)dx# ? ...

2016年1月30日 · int cos^6 x dx = 5/16 x + 1/4 sin 2x + 3/16 sin 4x -1/48 sin^3 2x int cos^6x dx We can rewrite this function as; int (cos^2x)^3dx Now we can rewrite cos^2 x using the half angle formula. int(1/2(1+cos(2x)))^3 dx If we expand the expression we can get rid of the exponent. 1/8 int (1 + 3cos(2x) + 3cos^2 (2x) + cos^3 (2x) )dx We can split up this expression using the sum rule. 1/8 int dx + 3/8 ...