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人気のある微分積分 >

integral of rcsin(sqrt(x))

解

\int d arcsin (x) d x

解

d x arcsin (x) - \frac{1}{2} d arcsin (x) + \frac{1}{4} d sin (2 arcsin (x)) + C

解答ステップ

\int d arcsin (x) d x

定数を除く:

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

= d \cdot \int arcsin (x) d x

u置換積分法を適用する

= d \cdot \int arcsin (u) \cdot 2 u d u

定数を除く:

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

= d \cdot 2 \cdot \int arcsin (u) u d u

部分積分を適用する

= d \cdot 2 (\frac{1}{2} u^{2} arcsin (u) - \int \frac{u ^{2}}{2 1 - u ^{2}} d u)

\int \frac{u ^{2}}{2 1 - u ^{2}} d u = \frac{1}{4} (arcsin (u) - \frac{1}{2} sin (2 arcsin (u)))

= d \cdot 2 (\frac{1}{2} u^{2} arcsin (u) - \frac{1}{4} (arcsin (u) - \frac{1}{2} sin (2 arcsin (u))))

代用を戻す

u = x

= d \cdot 2 (\frac{1}{2} (x)^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))))

簡素化

d \cdot 2 (\frac{1}{2} (x)^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))) : d x arcsin (x) - \frac{1}{2} d arcsin (x) + \frac{1}{4} d sin (2 arcsin (x))

= d x arcsin (x) - \frac{1}{2} d arcsin (x) + \frac{1}{4} d sin (2 arcsin (x))

定数を解答に追加する

= d x arcsin (x) - \frac{1}{2} d arcsin (x) + \frac{1}{4} d sin (2 arcsin (x)) + C

グラフ

人気の例

integral of (sqrt(5-θ^2))/(θ^2)

\int \frac{5 - θ ^{2}}{θ ^{2}} d θ

integral of arccos(5x)

\int arccos (5 x) d x

integral of-4cot(6x^2)2x

\int - 4 cot (6 x^{2}) 2 x d x

integral of-3/(1-2x)+2sin(5-6x)

\int - \frac{3}{1 - 2 x} + 2 sin (5 - 6 x) d x

integral of x^2-2x+4

\int x^{2} - 2 x + 4 d x