integral of (x^6+1)e^{x^7+7x}

解答

\int (x^{6} + 1) e^{x^{7} + 7 x} d x

\frac{1}{7} e^{x^{7} + 7 x} + C

求解步骤

\int (x^{6} + 1) e^{x^{7} + 7 x} d x

使用换元积分法

= \int \frac{e ^{u}}{7} d u

提出常数:

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

= \frac{1}{7} \cdot \int e^{u} d u

使用积分常见定则:

\int e^{u} d u = e^{u}

= \frac{1}{7} e^{u}

u = x^{7} + 7 x

代回

= \frac{1}{7} e^{x^{7} + 7 x}

解答补常数

= \frac{1}{7} e^{x^{7} + 7 x} + C

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