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人気のある微分積分 >

integral of 2xcos(9x)

解

\int 2 x cos (9 x) d x

解

\frac{2}{81} (9 x sin (9 x) + cos (9 x)) + C

解答ステップ

\int 2 x cos (9 x) d x

定数を除く:

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

= 2 \cdot \int x cos (9 x) d x

u置換積分法を適用する

= 2 \cdot \int \frac{u cos ( u )}{81} d u

定数を除く:

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

= 2 \cdot \frac{1}{81} \cdot \int u cos (u) d u

部分積分を適用する

= 2 \cdot \frac{1}{81} (u sin (u) - \int sin (u) d u)

\int sin (u) d u = - cos (u)

= 2 \cdot \frac{1}{81} (u sin (u) - (- cos (u)))

代用を戻す

u = 9 x

= 2 \cdot \frac{1}{81} (9 x sin (9 x) - (- cos (9 x)))

簡素化

2 \cdot \frac{1}{81} (9 x sin (9 x) - (- cos (9 x))) : \frac{2}{81} (9 x sin (9 x) + cos (9 x))

= \frac{2}{81} (9 x sin (9 x) + cos (9 x))

定数を解答に追加する

= \frac{2}{81} (9 x sin (9 x) + cos (9 x)) + C

グラフ

人気の例

tangent f(x)= 3/(x-2),\at x=3

t an g e n t f (x) = \frac{3}{x - 2}, at x = 3

integral from 0 to 4 of (3t)/((t-5)^2)

\int_{0}^{4} \frac{3 t}{( t - 5 ) ^{2}} d t

derivative f(x)= x/(x^2+6)

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 6}

limit as x approaches 2 of 5x^3-9x^2+1

x \to 2 lim (5 x^{3} - 9 x^{2} + 1)

limit as x approaches infinity of 4^xx

x \to \infty lim (4^{x} x)