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受欢迎的微积分 >

integral of 2xycos(xy^2)

解答

\int 2 x y cos (x y^{2}) d y

解答

sin (x y^{2}) + C

求解步骤

\int 2 x y cos (x y^{2}) d y

提出常数:

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

= 2 x \cdot \int cos (x y^{2}) y d y

使用换元积分法

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

提出常数:

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

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

使用换元积分法

= 2 x \frac{1}{2} \cdot \int \frac{cos ( v )}{x} d v

提出常数:

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

= 2 x \frac{1}{2} \cdot \frac{1}{x} \cdot \int cos (v) d v

使用积分常见定则:

\int cos (v) d v = sin (v)

= 2 x \frac{1}{2} \cdot \frac{1}{x} sin (v)

代回

= 2 x \frac{1}{2} \cdot \frac{1}{x} sin (x y^{2})

化简

2 x \frac{1}{2} \cdot \frac{1}{x} sin (x y^{2}) : sin (x y^{2})

= sin (x y^{2})

解答补常数

= sin (x y^{2}) + C

作图

流行的例子

derivative of a{r}(xc,x)

\frac{d}{d x} (a r (x) c, x)

y^{^{''}} - 8 y + 16 = 0

integral from-1 to 2 of x^3-2x

\int_{- 1}^{2} x^{3} - 2 x d x

integral of ln(3x+8)

\int ln (3 x + 8) d x

derivative of 1/(11x^{10/11})

\frac{d}{d x} (\frac{1}{11 x ^{\frac{10}{11}}})