Goniometrical primitives of functions

$\backslash \; int\; \backslash \; sin\; (ax+b)\; \backslash ,\; dx=-\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; cos\; (ax+b)+C$

$\backslash \; int\; \backslash \; cos\; (ax+b)\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; sin\; (ax+b)+C$

$\backslash \; int\; \backslash \; tan\; ax\; \backslash ,\; dx=-\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; ln|\backslash \; cos\; ax|+C$

$\backslash \; int\; \backslash \; operatorname\; \{cotan\}\; ax\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; ln|\backslash \; sin\; ax|+C$

$\backslash \; int\; \backslash \; frac\; \{1\}\; \{\backslash \; sin\; ax\}\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; ln\; \backslash \; left|\backslash \; tan\; \backslash \; frac\; \{ax\}\; \{2\}\; \backslash \; right|+C$

$\backslash \; int\; \backslash \; frac\; \{1\}\; \{\backslash \; cos\; ax\}\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; ln\; \backslash \; left|\backslash \; tan\; \backslash \; left\; (\backslash \; frac\; \{ax\}\; \{2\}\; +\; \backslash \; frac\; \{\backslash \; pi\}\; \{4\}\; \backslash \; right)\; \backslash \; right|+C$

$\backslash \; int\; \backslash \; sin^n\; ax\; \backslash ,\; dx=-\; \backslash \; frac\; \{1\}\; \{Na\}\; \backslash \; sin^\; \{n-1\}\; ax\; \backslash \; cos\; ax\; +\; \backslash \; frac\; \{n-1\}\; \{N\}\; \backslash \; int\; \backslash \; sin^\; \{N2\}\; ax\; \backslash ,\; dx$ (N ∈ ℤ \ {0, - 1})

$\backslash \; int\; \backslash \; cos^n\; ax\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{Na\}\; \backslash \; cos^\; \{n-1\}\; ax\; \backslash \; sin\; ax\; +\; \backslash \; frac\; \{n-1\}\; \{N\}\; \backslash \; int\; \backslash \; cos^\; \{N2\}\; ax\; \backslash ,\; dx$ (N ∈ ℤ \ {0, - 1})

$\backslash \; int\; \backslash \; tan^n\; ax\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{(n-1)\; has\}\; \backslash \; tan^\; \{n-1\}\; ax\; -\; \backslash \; int\; \backslash \; tan^\; \{N2\}\; ax\; \backslash ,\; dx$ (N ∈ ℕ \ {0,1})

$\backslash \; int\; \backslash \; operatorname\; \{cotan\}\; ^n\; ax\; \backslash ,\; dx=-\; \backslash \; frac\; \{1\}\; \{(n-1)\; has\}\; \backslash \; operatorname\; \{cotan\}\; ^\; \{n-1\}\; ax\; -\; \backslash \; int\; \backslash \; operatorname\; \{cotan\}\; ^\; \{N2\}\; ax\; \backslash ,\; dx$ (N ∈ ℕ \ {0,1})

$\backslash \; int\; x^n\; \backslash \; sin\; ax\; \backslash ,\; dx=-\; \backslash \; frac\{1\}\; \{has\}\; x^n\; \backslash \; cos\; ax\; +\; \backslash \; frac\; \{N\}\; \{has\}\; \backslash \; int\; x^\; \{n-1\}\; \backslash \; cos\; ax\; \backslash ,\; dx$ (N ∈ ℤ \ {- 1})

$\backslash \; int\; x^n\; \backslash \; cos\; ax\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; x^n\; \backslash \; sin\; ax\; -\; \backslash \; frac\; \{N\}\; \{has\}\; \backslash \; int\; x^\; \{n-1\}\; \backslash \; sin\; ax\; \backslash ,\; dx$ (N ∈ ℤ \ {- 1})

$\backslash \; int\; \backslash \; frac\; \{\backslash \; sin\; \backslash ,\; ax\}\; \{X\}\; \backslash ,\; dx=\; \backslash \; sum\_\; \{n=0\}\; ^\{+\; \backslash \; infty\}\; \backslash \; frac\; \{(ax)\; ^\; \{2n+1\}\}\; \{(2n+1)\; (2n+1)!\}+C$

$\backslash \; int\; \backslash \; frac\; \{\backslash \; cos\; \backslash ,\; ax\}\; \{X\}\; \backslash ,\; dx=\; \backslash \; ln|ax|+\; \backslash \; sum\_\; \{n=1\}\; ^\; \{+\; \backslash \; infty\}\; (-\; 1)\; ^n\; \backslash \; frac\; \{(ax)\; ^\; \{2n\}\}\; \{2n\; (2n)!\}+C$

$\backslash \; int\; \backslash \; frac\; \{1\}\; \{1+\; \backslash \; sin\; ax\}\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; tan\; \backslash \; left\; (\backslash \; frac\; \{ax\}\; \{2\}\; -\; \backslash \; frac\; \{\backslash \; pi\}\; \{4\}\; \backslash \; right)\; +C$

$\backslash \; int\; \backslash \; frac\; \{1\}\; \{1\; \backslash \; sin\; ax\}\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; tan\; \backslash \; left\; (\backslash \; frac\; \{ax\}\; \{2\}\; +\; \backslash \; frac\; \{\backslash \; pi\}\; \{4\}\; \backslash \; right)\; +C$

$\backslash \; int\; \backslash \; frac\; \{1\}\; \{1+\; \backslash \; cos\; ax\}\; \backslash ,\; dx=\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; tan\; \backslash \; frac\; \{ax\}\; \{2\}\; +C$

$\backslash \; int\; \backslash \; frac\; \{1\}\; \{1\; \backslash \; cos\; ax\}\; \backslash ,\; dx=-\; \backslash \; frac\; \{1\}\; \{has\}\; \backslash \; operatorname\; \{cotan\}\; \backslash \; frac\; \{ax\}\; \{2\}\; +C$

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