integral of (sin(θ)-cos(θ))

解答

\int (sin (θ) - cos (θ)) d θ

- cos (θ) - sin (θ) + C

求解步骤

\int sin (θ) - cos (θ) d θ

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 sin (θ) d θ - \int cos (θ) d θ

\int sin (θ) d θ = - cos (θ)

\int cos (θ) d θ = sin (θ)

= - cos (θ) - sin (θ)

解答补常数

= - cos (θ) - sin (θ) + C

\int x (e^{- x^{2}}) d x

\int (x)^{7} d x

\int \frac{cos ( ln ( t ) )}{5 t} d t

\int (2 x^{4} + 6)^{\frac{4}{3}} x^{3} d x

\int \frac{x ^{5} + 9 x ^{3} - 9 x ^{2} - 9}{x ^{3} + 9 x} d x