integral of ((cos^3(x)+1)/(cos^2(x)))

解

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

sin (x) + tan (x) + C

解答ステップ

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

拡張

\frac{cos ^{3} ( x ) + 1}{cos ^{2} ( x )} : cos (x) + \frac{1}{cos ^{2} ( x )}

= \int cos (x) + \frac{1}{cos ^{2} ( x )} d x

総和規則を適用する:

\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 \frac{1}{cos ^{2} ( x )} d x

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

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= sin (x) + tan (x)

定数を解答に追加する

= sin (x) + tan (x) + C