integral of 2x^2cos(2pi)x^3

解答

\int 2 x^{2} cos (2 π) x^{3} d x

\frac{x ^{6}}{3} + C

求解步骤

\int 2 x^{2} cos (2 π) x^{3} d x

提出常数:

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

= 2 cos (2 π) \cdot \int x^{2} x^{3} d x

2 cos (2 π) = 2

= 2 \cdot \int x^{2} x^{3} d x

化简

x^{2} x^{3} : x^{5}

= 2 \cdot \int x^{5} d x

使用幂法则

= 2 \cdot \frac{x ^{6}}{6}

化简

2 \cdot \frac{x ^{6}}{6} : \frac{x ^{6}}{3}

= \frac{x ^{6}}{3}

解答补常数

= \frac{x ^{6}}{3} + C

\int \frac{y ^{3} - y ^{2} + 1}{( y ^{2} + 2 y + 2 ) ^{2}} d y

\int (4 x + 7)^{9} d x

\int \frac{1}{( x - 1 ) ^{2} ( x + 4 ) ^{2}} d x

\int (\frac{5}{t} + 4 e^{t}) d t

\int cos (x) cos (π sin (x)) d x