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I know that

[tex]\int \tan^{2}x dx= \int \sec^{2}x-1\ dx = \tan x - x + C[/tex]

but i don't completely understand how this is derived. Because of this lack of comprehension, I have no idea what to do with [tex]\int \sec^{4}5x\ dx[/tex]. I went from there to get:

[tex]\int \sec^{4}5x\ dx=[/tex]

[tex]\int [\sec^{2}5x]^{2}\ dx=[/tex]

[tex]\int \tan^{2}5x\ dx = [/tex]

but I have no idea where to go from here. Any help would be appreciated. Thanks in advance.

[tex]\int \tan^{2}x dx= \int \sec^{2}x-1\ dx = \tan x - x + C[/tex]

but i don't completely understand how this is derived. Because of this lack of comprehension, I have no idea what to do with [tex]\int \sec^{4}5x\ dx[/tex]. I went from there to get:

[tex]\int \sec^{4}5x\ dx=[/tex]

[tex]\int [\sec^{2}5x]^{2}\ dx=[/tex]

[tex]\int \tan^{2}5x\ dx = [/tex]

but I have no idea where to go from here. Any help would be appreciated. Thanks in advance.

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