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人気のある微分積分 >

integral of (7x^3)/(sqrt(4+x^2))

解

\int \frac{7 x ^{3}}{4 + x ^{2}} d x

解

7 (\frac{1}{3} (4 + x^{2})^{\frac{3}{2}} - 4 4 + x^{2}) + C

解答ステップ

\int \frac{7 x ^{3}}{4 + x ^{2}} d x

定数を除く:

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

= 7 \cdot \int \frac{x ^{3}}{4 + x ^{2}} d x

u置換積分法を適用する

= 7 \cdot \int u^{2} - 4 d u

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

= 7 (\int u^{2} d u - \int 4 d u)

\int u^{2} d u = \frac{u ^{3}}{3}

\int 4 d u = 4 u

= 7 (\frac{u ^{3}}{3} - 4 u)

代用を戻す

u = 4 + x^{2}

= 7 (\frac{( 4 + x ^{2} ) ^{3}}{3} - 4 4 + x^{2})

簡素化

7 (\frac{( 4 + x ^{2} ) ^{3}}{3} - 4 4 + x^{2}) : 7 (\frac{1}{3} (4 + x^{2})^{\frac{3}{2}} - 4 4 + x^{2})

= 7 (\frac{1}{3} (4 + x^{2})^{\frac{3}{2}} - 4 4 + x^{2})

定数を解答に追加する

= 7 (\frac{1}{3} (4 + x^{2})^{\frac{3}{2}} - 4 4 + x^{2}) + C

グラフ

人気の例

tangent y=-2x^3,(1,-2)

t an g e n t y = - 2 x^{3}, (1, - 2)

integral of (3x^2)

\int (3 x^{2}) d x

(\partial)/(\partial x)(sin^2(3xy^2-y))

\frac{\partial}{\partial x} (sin^{2} (3 x y^{2} - y))

implicit (dy)/(dx),y=11^x

im pl i c i t \frac{d y}{d x}, y = 1 1^{x}

derivative of (x^2-3e^x)

\frac{d}{d x} ((x^{2} - 3) e^{x})