∫sinnx dx=−1nsinn−1xcosx+n−1n∫sinn−2x dx\int \sin^{n}x \, dx=-\frac{1}{n}\sin^{n-1}x\cos{x}+\frac{n-1}{n}\int \sin^{n-2}x \, dx∫sinnxdx=−n1sinn−1xcosx+nn−1∫sinn−2xdx
∫cosnx dx=1ncosn−1xsinx+n−1n∫cosn−2x dx\int \cos^{n}x \, dx=\frac{1}{n}\cos^{n-1}x\sin{x}+\frac{n-1}{n}\int \cos^{n-2}x \, dx∫cosnxdx=n1cosn−1xsinx+nn−1∫cosn−2xdx
∫tannx dx=1n−1tann−1x−∫tann−2x dx\int \tan^{n}x \, dx=\frac{1}{n-1}\tan^{n-1}x-\int \tan^{n-2}x \, dx∫tannxdx=n−11tann−1x−∫tann−2xdx
∫cotnx dx=−1n−1cotn−1x−∫cotn−2x dx\int \cot^{n}x \, dx=-\frac{1}{n-1}\cot^{n-1}x-\int \cot^{n-2}x \, dx∫cotnxdx=−n−11cotn−1x−∫cotn−2xdx
∫secnx dx=1n−1secn−2xtanx+n−2n−1∫secn−2x dx\int \sec^{n}x \, dx=\frac{1}{n-1}\sec^{n-2}x\tan{x}+\frac{n-2}{n-1}\int \sec^{n-2}x \, dx∫secnxdx=n−11secn−2xtanx+n−1n−2∫secn−2xdx
∫cscnx dx=−1n−1cscn−2xcotx+n−2n−1∫cscn−2x dx\int \csc^{n}x \, dx=-\frac{1}{n-1}\csc^{n-2}x\cot{x}+\frac{n-2}{n-1}\int \csc^{n-2}x \, dx∫cscnxdx=−n−11cscn−2xcotx+n−1n−2∫cscn−2xdx
繁體中文
三角降次公式