integral of (cos(sqrt(x+1)))/(sqrt(x+1))

解答

\int \frac{cos ( x + 1 )}{x + 1} d x

2 sin (x + 1) + C

求解步骤

\int \frac{cos ( x + 1 )}{x + 1} d x

使用换元积分法

= \int 2 cos (u) d u

提出常数:

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

= 2 \cdot \int cos (u) d u

使用积分常见定则:

\int cos (u) d u = sin (u)

= 2 sin (u)

u = x + 1

代回

= 2 sin (x + 1)

解答补常数

= 2 sin (x + 1) + C