integral of sin^8(3/4)x*cos^6(3/4)x

解答

\int sin^{8} (\frac{3}{4}) x \cdot cos^{6} (\frac{3}{4}) x d x

\frac{sin ^{8} ( \frac{3}{4} ) cos ^{6} ( \frac{3}{4} ) x ^{3}}{3} + C

求解步骤

\int sin^{8} (\frac{3}{4}) x cos^{6} (\frac{3}{4}) x d x

提出常数:

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

= sin^{8} (\frac{3}{4}) cos^{6} (\frac{3}{4}) \cdot \int xx d x

化简

xx : x^{2}

= sin^{8} (\frac{3}{4}) cos^{6} (\frac{3}{4}) \cdot \int x^{2} d x

使用幂法则

= sin^{8} (\frac{3}{4}) cos^{6} (\frac{3}{4}) \frac{x ^{3}}{3}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sin ^{8} ( \frac{3}{4} ) cos ^{6} ( \frac{3}{4} ) x ^{3}}{3}

解答补常数

= \frac{sin ^{8} ( \frac{3}{4} ) cos ^{6} ( \frac{3}{4} ) x ^{3}}{3} + C

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