integral of xsin(4)x^2

解答

\int x sin (4) x^{2} d x

\frac{1}{4} sin (4) x^{4} + C

求解步骤

\int x sin (4) x^{2} d x

提出常数:

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

= sin (4) \cdot \int x x^{2} d x

化简

x x^{2} : x^{3}

= sin (4) \cdot \int x^{3} d x

使用幂法则

= sin (4) \frac{x ^{4}}{4}

化简

sin (4) \frac{x ^{4}}{4} : \frac{1}{4} sin (4) x^{4}

= \frac{1}{4} sin (4) x^{4}

解答补常数

= \frac{1}{4} sin (4) x^{4} + C

l a pl a ce t r an s f or m f (t) = t^{2} - 2 t

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