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受欢迎的微积分 >

integral of (7cos(sqrt(x)))

解答

\int (7 cos (x)) d x

解答

14 (x sin (x) + cos (x)) + C

求解步骤

\int 7 cos (x) d x

提出常数:

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

= 7 \cdot \int cos (x) d x

使用换元积分法

= 7 \cdot \int cos (u) \cdot 2 u d u

提出常数:

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

= 7 \cdot 2 \cdot \int cos (u) u d u

使用分布积分法

= 7 \cdot 2 (u sin (u) - \int sin (u) d u)

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

= 7 \cdot 2 (u sin (u) - (- cos (u)))

u = x

代回

= 7 \cdot 2 (x sin (x) - (- cos (x)))

化简

= 14 (x sin (x) + cos (x))

解答补常数

= 14 (x sin (x) + cos (x)) + C

作图

流行的例子

derivative of log_{2x+1}(2x+3)

\frac{d}{d x} (lo g_{2 x + 1} (2 x + 3))

(\partial)/(\partial x)(3e^{x^3y^3})

\frac{\partial}{\partial x} (3 e^{x^{3} y^{3}})

tangent sqrt(7x+4)

t an g e n t 7 x + 4

integral of 2x(x^2+2)^4

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

laplacetransform 7sin(4t+8)+3cos(4t-2)

l a pl a ce t r an s f or m 7 sin (4 t + 8) + 3 cos (4 t - 2)