integral of x-xcos(x)

解答

\int x - x cos (x) d x

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

求解步骤

\int x - x cos (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 x d x - \int x cos (x) d x

\int x d x = \frac{x ^{2}}{2}

\int x cos (x) d x = x sin (x) + cos (x)

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

化简

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

解答补常数

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

\int \frac{1}{x + x - 1} d x

\int 4 (3 r^{4} + 1)^{3} r^{3} d r

\int 1 - cos (u) d u

\int \frac{3 x ^{2} - 1}{x ^{3} + x ^{2}} d x

\int 2 x + 3 x^{1.7} d x