integral of (1+sin(t))^9cos(t)

解答

\int (1 + sin (t))^{9} cos (t) d t

\frac{( 1 + sin ( t ) ) ^{10}}{10} + C

求解步骤

\int (1 + sin (t))^{9} cos (t) d t

使用换元积分法

= \int u^{9} d u

使用幂法则

= \frac{u ^{10}}{10}

u = 1 + sin (t)

代回

= \frac{( 1 + sin ( t ) ) ^{10}}{10}

解答补常数

= \frac{( 1 + sin ( t ) ) ^{10}}{10} + C

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