integral of 10.2+2.5x+0.1x^2

解答

\int 10.2 + 2.5 x + 0.1 x^{2} d x

10.2 x + 1.25 x^{2} + 0.03333 \dots x^{3} + C

求解步骤

\int 10.2 + 2.5 x + 0.1 x^{2} 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 10.2 d x + \int 2.5 x d x + \int 0.1 x^{2} d x

\int 10.2 d x = 10.2 x

\int 2.5 x d x = 1.25 x^{2}

\int 0.1 x^{2} d x = 0.03333 \dots x^{3}

= 10.2 x + 1.25 x^{2} + 0.03333 \dots x^{3}

解答补常数

= 10.2 x + 1.25 x^{2} + 0.03333 \dots x^{3} + C

\int a + b x + x^{5} d x

in t e g r a l x^{- 4}

\int \frac{tan ( 3 x ) - cot ( 3 x )}{sin ( 3 x )} d x

\int \frac{1}{( x + 2 ) ln ( x + 2 )} d x

\int cos^{3} (x) - 1 d x