integral of cos(x)+(x^2+1)^7*2x

解答

\int cos (x) + (x^{2} + 1)^{7} \cdot 2 x d x

sin (x) + \frac{1}{8} (x^{2} + 1)^{8} + C

求解步骤

\int cos (x) + (x^{2} + 1)^{7} \cdot 2 x 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 cos (x) d x + \int (x^{2} + 1)^{7} \cdot 2 x d x

\int cos (x) d x = sin (x)

\int (x^{2} + 1)^{7} \cdot 2 x d x = \frac{1}{8} (x^{2} + 1)^{8}

= sin (x) + \frac{1}{8} (x^{2} + 1)^{8}

解答补常数

= sin (x) + \frac{1}{8} (x^{2} + 1)^{8} + C

im pl i c i t \frac{d y}{d x}, ln (x y^{3}) = x y

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

d er i v a t i v e f (x) = cos^{5} (x)

d er i v a t i v e arcsec (\frac{1}{4 t ^{5}})

n = 0 \sum \infty \frac{z ^{n}}{n ^{2}}