integral of sin(1/10)xsin(1/20)x

解答

\int sin (\frac{1}{10}) x sin (\frac{1}{20}) x d x

\frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3} + C

求解步骤

\int sin (\frac{1}{10}) x sin (\frac{1}{20}) x d x

提出常数:

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

= sin (\frac{1}{10}) sin (\frac{1}{20}) \cdot \int xx d x

化简

xx : x^{2}

= sin (\frac{1}{10}) sin (\frac{1}{20}) \cdot \int x^{2} d x

使用幂法则

= sin (\frac{1}{10}) sin (\frac{1}{20}) \frac{x ^{3}}{3}

化简

sin (\frac{1}{10}) sin (\frac{1}{20}) \frac{x ^{3}}{3} : \frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3}

= \frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3}

解答补常数

= \frac{1}{3} sin (\frac{1}{10}) sin (\frac{1}{20}) x^{3} + C

x \to 4 + lim (5 x^{2} + x)

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\int \frac{8 - 5 x}{x ^{2} - 12 x - 32} d x

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{13}{2}}} d t

x \to 0 lim (\frac{tan ( 2 x )}{x})