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受欢迎的微积分 >

integral of 4xsin(2x^2)

解答

\int 4 x sin (2 x^{2}) d x

解答

- cos (2 x^{2}) + C

求解步骤

\int 4 x sin (2 x^{2}) d x

提出常数:

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

= 4 \cdot \int x sin (2 x^{2}) d x

使用换元积分法

= 4 \cdot \int \frac{sin ( u )}{4} d u

提出常数:

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

= 4 \cdot \frac{1}{4} \cdot \int sin (u) d u

使用积分常见定则:

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

= 4 \cdot \frac{1}{4} (- cos (u))

u = 2 x^{2}

代回

= 4 \cdot \frac{1}{4} (- cos (2 x^{2}))

化简

4 \cdot \frac{1}{4} (- cos (2 x^{2})) : - cos (2 x^{2})

= - cos (2 x^{2})

解答补常数

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

作图

流行的例子

(\partial)/(\partial x)(x^6+8xy^5)

\frac{\partial}{\partial x} (x^{6} + 8 x y^{5})

(\partial)/(\partial x)(3x+4y)

\frac{\partial}{\partial x} (3 x + 4 y)

laplacetransform (25t)((t^2)/(25))

l a pl a ce t r an s f or m (25 t) (\frac{t ^{2}}{25})

derivative y=(x^2+sin(x))^3

d er i v a t i v e y = (x^{2} + sin (x))^{3}

tangent f(x)=\sqrt[4]{x}-x,(1,0)

t an g e n t f (x) = 4 x - x, (1, 0)