integral of x^6+e^{2x}

解答

\int x^{6} + e^{2 x} d x

\frac{x ^{7}}{7} + \frac{1}{2} e^{2 x} + C

求解步骤

\int x^{6} + e^{2 x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{6} d x + \int e^{2 x} d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int e^{2 x} d x = \frac{1}{2} e^{2 x}

= \frac{x ^{7}}{7} + \frac{1}{2} e^{2 x}

解答补常数

= \frac{x ^{7}}{7} + \frac{1}{2} e^{2 x} + C

\int (10 - 20 x^{4}) csc^{2} (2 x^{5} - 5 x) d x

\frac{\partial}{\partial y} (ln (x - y))

\frac{d}{d x} (x (e^{x} - 1))

\frac{d}{d x} (- ln (x^{4}))

\int 1 + cos (π θ) d θ