integral of (e^{2y}-ycos(x)y)

解答

\int (e^{2 y} - y cos (x) y) d x

e^{2 y} x - y^{2} sin (x) + C

求解步骤

\int e^{2 y} - y cos (x) y d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{2 y} d x - \int cos (x) yy d x

\int e^{2 y} d x = e^{2 y} x

\int cos (x) yy d x = y^{2} sin (x)

= e^{2 y} x - y^{2} sin (x)

解答补常数

= e^{2 y} x - y^{2} sin (x) + C

sin (y) csc (x) (\frac{d y}{d x}) = 1

t an g e n t f (x) = x^{2} - 8 x + 9, at x = 3

\int_{0}^{1} \frac{2}{1 + t ^{2}} d t

\int \frac{12}{1 - cos ( 4 x )} d x

n = 0 \sum \infty \frac{1}{6}