integral of 7sin^6(x)cos(x)

解答

\int 7 sin^{6} (x) cos (x) d x

sin^{7} (x) + C

求解步骤

\int 7 sin^{6} (x) cos (x) d x

提出常数:

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

= 7 \cdot \int sin^{6} (x) cos (x) d x

使用换元积分法

= 7 \cdot \int u^{6} d u

使用幂法则

= 7 \cdot \frac{u ^{7}}{7}

u = sin (x)

代回

= 7 \cdot \frac{sin ^{7} ( x )}{7}

化简

7 \cdot \frac{sin ^{7} ( x )}{7} : sin^{7} (x)

= sin^{7} (x)

解答补常数

= sin^{7} (x) + C

\int \frac{1}{e ^{2 y} - 2 e ^{y}} d y

d er i v a t i v e f (x) = 6^{x} lo g_{5} (x)

\int_{0}^{2 π} cos^{2} (x) d x

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

\int 3 1 - x d x