Find ∫ xcos & # 178; X DX

Find ∫ xcos & # 178; X DX

∫xcos²x dx
=∫x*(1+cos2x)/2dx
=∫x/2dx+∫xcos2x/2dx
=x^2/4+ ∫x/4dsin2x
=x^2/4+ x*sin2x/4 -∫sin2xdx/4
=X ^ 2 / 4 + X * sin2x / 4 + cos2x / 8 + C (constant)

∫(2x+x²) dx

∫(2x+x²) dx
=x^2+x^3/3+C

Given √ 25-x & # 178; + 15-x & # 178; = 2, find the value of √ 25-x & # 178; + 15-x & # 178
More intuitive: given the value of √ (25-x & # 178;) + 15-x & # 178;) = 2, find the value of √ (25-x & # 178;) + 15-x & # 178;)

（√25-x2 + √15-x2）（ √25-x2 - √15-x2 ）
=（25-x2）-（15-x2）
=10
So √ 25-x2 + √ 15-x2 = 10 ÷ 2 = 5 is the best~