integral of sin(x)(2cos(x))

解答

\int sin (x) (2 cos (x)) d x

sin^{2} (x) + C

求解步骤

\int sin (x) \cdot 2 cos (x) d x

提出常数:

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

= 2 \cdot \int sin (x) cos (x) d x

使用换元积分法

= 2 \cdot \int u d u

使用幂法则

= 2 \cdot \frac{u ^{2}}{2}

u = sin (x)

代回

= 2 \cdot \frac{sin ^{2} ( x )}{2}

化简

2 \cdot \frac{sin ^{2} ( x )}{2} : sin^{2} (x)

= sin^{2} (x)

解答补常数

= sin^{2} (x) + C

\int csc^{5} (x) cot^{5} (x) d x

\int x 8 + 2 x - x^{2} d x

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

\int sec (\frac{1}{2}) z tan (\frac{1}{2}) z d z

\int e^{s e c (w)} sec (w) tan (w) d w