integral of (cos(x))/(5+sin(x))

解答

\int \frac{cos ( x )}{5 + sin ( x )} d x

ln ∣ 5 + sin (x) ∣ + C

求解步骤

\int \frac{cos ( x )}{5 + sin ( x )} d x

使用换元积分法

= \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

u = 5 + sin (x)

代回

= ln ∣ 5 + sin (x) ∣

解答补常数

= ln ∣ 5 + sin (x) ∣ + C

d er i v a t i v e 11 t^{2} + 9

\int_{0}^{3} \frac{1}{x ^{2} - 6 x + 5} d x

d er i v a t i v e \frac{6 x}{( x ^{2} + 3 ) ^{2}}

d er i v a t i v e y = 7^{x + a r c c o s (x)}

a re a x^{2} - 4 x, 2 x - x^{2}