integral of-3sin(x)

解答

\int - 3 sin (x) d x

3 cos (x) + C

求解步骤

\int - 3 sin (x) d x

提出常数:

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

= - 3 \cdot \int sin (x) d x

使用积分常见定则:

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

= - 3 (- cos (x))

化简

= 3 cos (x)

解答补常数

= 3 cos (x) + C

e x p an d x (x^{2} + 1)^{10}

\int_{1}^{5} (x - 3) d x

d er i v a t i v e \frac{1}{t ^{2} + 6 t - 2}

\frac{d}{d x} (x^{4} + 3 x^{2} - 6)

x \to 0 lim (\frac{5 x}{x ^{2} + 5 x})