integral of ax^3+6/(x^2)

解答

\int a x^{3} + \frac{6}{x ^{2}} d x

\frac{a x ^{4}}{4} - \frac{6}{x} + C

求解步骤

\int a x^{3} + \frac{6}{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 a x^{3} d x + \int \frac{6}{x ^{2}} d x

\int a x^{3} d x = \frac{a x ^{4}}{4}

\int \frac{6}{x ^{2}} d x = - \frac{6}{x}

= \frac{a x ^{4}}{4} - \frac{6}{x}

解答补常数

= \frac{a x ^{4}}{4} - \frac{6}{x} + C

\int \frac{cos ^{4} ( x )}{sin ^{4} ( x )} d x

\int (3 x^{2} - 5 x + 3) d x

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\int \frac{x ^{6}}{( 3 + x ^{7} ) ^{2}} d x