integral of (2x+7)

解答

\int (2 x + 7) d x

x^{2} + 7 x + C

求解步骤

\int 2 x + 7 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 2 x d x + \int 7 d x

\int 2 x d x = x^{2}

\int 7 d x = 7 x

= x^{2} + 7 x

解答补常数

= x^{2} + 7 x + C

\int \frac{y}{x ^{5} + 1} d y

\int (\frac{x + 1}{x}) d x

\int (\frac{y}{2 x + 3 y}) d x

\int \frac{e ^{2 t}}{1 + 6 e ^{2 t} + 9 e ^{4 t}} d t

\int 7 x e^{0.005 x^{2}} d x