integral of r^2sec^2(r^3)

解答

\int r^{2} sec^{2} (r^{3}) d r

\frac{1}{3} tan (r^{3}) + C

求解步骤

\int r^{2} sec^{2} (r^{3}) d r

使用换元积分法

= \int \frac{sec ^{2} ( u )}{3} d u

提出常数:

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

= \frac{1}{3} \cdot \int sec^{2} (u) d u

使用积分常见定则:

\int sec^{2} (u) d u = tan (u)

= \frac{1}{3} tan (u)

u = r^{3}

代回

= \frac{1}{3} tan (r^{3})

解答补常数

= \frac{1}{3} tan (r^{3}) + C

t an g e n t - 6 + 250 x^{3} - 3 x^{5}

\frac{d}{d x} (\frac{1}{5 x + 1})

x \to - 1 f lim (x)

a re a g (x) = x^{2}, g (x) = x^{k} 0, 1

\int \frac{3 x + 1}{( x ^{2} + 2 ) ( x + 3 )} d x