integral of c^{ax}

解答

\int c^{a x} d x

\frac{c ^{a x}}{a ln ( c )} + C

求解步骤

\int c^{a x} d x

使用换元积分法

= \int \frac{c ^{u}}{a} d u

提出常数:

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

= \frac{1}{a} \cdot \int c^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{1}{a} \cdot \frac{c ^{u}}{ln ( c )}

u = a x

代回

= \frac{1}{a} \cdot \frac{c ^{a x}}{ln ( c )}

化简

\frac{1}{a} \cdot \frac{c ^{a x}}{ln ( c )} : \frac{c ^{a x}}{a ln ( c )}

= \frac{c ^{a x}}{a ln ( c )}

解答补常数

= \frac{c ^{a x}}{a ln ( c )} + C

\int \frac{5}{x \cdot x ^{5} + 4} d x

\int \frac{8 x + 6}{( 4 x ^{2} + 6 x ) ^{3}} d x

\int ∣ x + 3 ∣ d x

\int (x^{3} x) d x

\int (3 + tan^{2} (θ)) d θ