integral of 2sin(θ)cos(θ)

解答

\int 2 sin (θ) cos (θ) d θ

sin^{2} (θ) + C

求解步骤

\int 2 sin (θ) cos (θ) d θ

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int sin (θ) cos (θ) d θ

使用换元积分法

= 2 \cdot \int u d u

使用幂法则

= 2 \cdot \frac{u ^{2}}{2}

u = sin (θ)

代回

= 2 \cdot \frac{sin ^{2} ( θ )}{2}

化简

2 \cdot \frac{sin ^{2} ( θ )}{2} : sin^{2} (θ)

= sin^{2} (θ)

解答补常数

= sin^{2} (θ) + C

\frac{d}{d x} (\frac{x + 3}{x})

t an g e n t f (x) = x^{3} - 2 x^{2}

x \to \infty lim (- 5 x)

x^{4} + y^{3} x^{5} + 4 y^{^{'}} = 0, y (0) = 0

\frac{\partial}{\partial x} (\frac{x y}{x ^{2} + y ^{2}})