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人気のある微分積分 >

integral of (cot(b)θ+tan(b)θ)^2

解

\int (cot (b) θ + tan (b) θ)^{2} d θ

解

\frac{θ ^{3}}{3 sin ^{2} ( b ) cos ^{2} ( b )} + C

解答ステップ

\int (cot (b) θ + tan (b) θ)^{2} d θ

三角関数の公式を使用して書き換える

= \int \frac{( θ cos ^{2} ( b ) + θ sin ^{2} ( b ) ) ^{2}}{sin ^{2} ( b ) cos ^{2} ( b )} d θ

定数を除く:

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

= \frac{1}{sin ^{2} ( b ) cos ^{2} ( b )} \cdot \int (θ cos^{2} (b) + θ sin^{2} (b))^{2} d θ

簡素化

θ cos^{2} (b) + θ sin^{2} (b) : θ

= \frac{1}{sin ^{2} ( b ) cos ^{2} ( b )} \cdot \int θ^{2} d θ

べき乗則を適用する

= \frac{1}{sin ^{2} ( b ) cos ^{2} ( b )} \cdot \frac{θ ^{3}}{3}

簡素化

\frac{1}{sin ^{2} ( b ) cos ^{2} ( b )} \cdot \frac{θ ^{3}}{3} : \frac{θ ^{3}}{3 sin ^{2} ( b ) cos ^{2} ( b )}

= \frac{θ ^{3}}{3 sin ^{2} ( b ) cos ^{2} ( b )}

定数を解答に追加する

= \frac{θ ^{3}}{3 sin ^{2} ( b ) cos ^{2} ( b )} + C

グラフ

人気の例

sum from n=0 to infinity of (9n!)/(n^n)

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