integral of 1/(cos^2(ay))

解答

\int \frac{1}{cos ^{2} ( a y )} d y

\frac{1}{a} tan (a y) + C

求解步骤

\int \frac{1}{cos ^{2} ( a y )} d y

使用基本三角恒等式:

\frac{1}{cos ( x )} = sec (x)

= \int sec^{2} (a y) d y

使用换元积分法

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

提出常数:

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

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

u = a y

代回

= \frac{1}{a} tan (a y)

解答补常数

= \frac{1}{a} tan (a y) + C

\frac{\partial}{\partial x} (8 x^{2} + y^{2} - 9 y)

t an g e n t f (x) = x^{2} + 3 x + 1, at x = 4

x \to 0 lim (ln (0))

\int x^{3} (3 + x^{4})^{5} d x

\frac{\partial}{\partial x} (2 x^{2} y + 3)