integral of e^{0.03x}

解答

\int e^{0.03 x} d x

33.33333 \dots e^{0.03 x} + C

求解步骤

\int e^{0.03 x} d x

使用换元积分法

= \int e^{u} \frac{1}{0.03} d u

提出常数:

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

= \frac{1}{0.03} \cdot \int e^{u} d u

化简

= 33.33333 \dots \cdot \int e^{u} d u

使用积分常见定则:

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

= 33.33333 \dots e^{u}

u = 0.03 x

代回

= 33.33333 \dots e^{0.03 x}

解答补常数

= 33.33333 \dots e^{0.03 x} + C

\int (x^{4} - 5 x^{2} - 6 x)^{4} (4 x^{3} - 10 x - 6) d x

\int \frac{8 x - 11}{5 + 2 x - x ^{2}} d x

\int \frac{x + 2}{2 x ^{2} + x + 1} d x

\int csc (x) csc^{2} (x) d x

\int \frac{ln ( x )}{5 x ^{2}} d x