integral of (tan(2x))^2

解答

\int (tan (2 x))^{2} d x

- x + \frac{1}{2} tan (2 x) + C

求解步骤

\int (tan (2 x))^{2} d x

化简

= \int tan^{2} (2 x) d x

使用三角恒等式改写

= \int - 1 + sec^{2} (2 x) d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d x + \int sec^{2} (2 x) d x

\int 1 d x = x

\int sec^{2} (2 x) d x = \frac{1}{2} tan (2 x)

= - x + \frac{1}{2} tan (2 x)

解答补常数

= - x + \frac{1}{2} tan (2 x) + C

\int_{0}^{\frac{1}{300}} 94 sin (225) d t

\int \frac{2}{t ^{3}} d t

x \to 0 lim (\frac{6 - 6 cos ( x )}{3})

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d er i v a t i v e lo g_{10} (x)