integral of 2xsin(x^2)+1/(x^2)sin(1/x)

解

\int 2 x sin (x^{2}) + \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

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

解答ステップ

\int 2 x sin (x^{2}) + \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

総和規則を適用する:

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

= \int 2 x sin (x^{2}) d x + \int \frac{1}{x ^{2}} sin (\frac{1}{x}) d x

\int 2 x sin (x^{2}) d x = - cos (x^{2})

\int \frac{1}{x ^{2}} sin (\frac{1}{x}) d x = cos (\frac{1}{x})

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

定数を解答に追加する

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