integral of 5sin(x^4)

解答

\int 5 sin (x^{4}) d x

i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4})) + C

求解步骤

\int 5 sin (x^{4}) d x

提出常数:

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

= 5 \cdot \int sin (x^{4}) d x

这是非初等函数积分:

\int sin (x^{4}) d x = \frac{1}{8} i x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

= 5 \cdot \frac{1}{8} i x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

化简

5 \cdot \frac{1}{8} i x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4})) : i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

= i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4}))

解答补常数

= i \frac{5}{8} x (E_{\frac{3}{4}} (- i x^{4}) - E_{\frac{3}{4}} (i x^{4})) + C

\int (5 x^{2} + 6 x^{- 2}) d x

\int \frac{1}{x ln ^{p} ( x )} d x

\int (sec (m x) + tan (m x))^{2} d x

\int (5 x^{3} + 2 x + \frac{1}{x ^{3}}) d x

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