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受欢迎的微积分 >

integral of (sin(5x))

解答

\int (sin (5 x)) d x

解答

- \frac{1}{5} cos (5 x) + C

求解步骤

\int sin (5 x) d x

使用换元积分法

= \int sin (u) \frac{1}{5} d u

提出常数:

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

= \frac{1}{5} \cdot \int sin (u) d u

使用积分常见定则:

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

= \frac{1}{5} (- cos (u))

u = 5 x

代回

= \frac{1}{5} (- cos (5 x))

化简

= - \frac{1}{5} cos (5 x)

解答补常数

= - \frac{1}{5} cos (5 x) + C

作图

流行的例子

integral of 9(tan(x))(ln(cos(x)))

\int 9 (tan (x)) (ln (cos (x))) d x

tangent f(x)=8xtan(x),\at x=pi

t an g e n t f (x) = 8 x tan (x), at x = π

f (x) = 3 - x

4y^{''}-20y^'+25y=0

4 y^{^{''}} - 20 y^{^{'}} + 25 y = 0

derivative of x^2sqrt(4-x)

\frac{d}{d x} (x^{2} 4 - x)