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We have to find the integral of sin (7x +5)
We first substitute 7x +5 with y. Now differentiate y with respect to x, we get dy = 7 dx. Substitute these in the given expression.
Int [sin (7x +5) dx]
=> Int [sin y * (1/7) dy]
=> 1/7 Int [sin y dy]
=> 1/7 (- cos y) +C
replace y with the 7x +5 again
=> (1/7) [- cos (7x +5)] + C
=> (-1/7) cos (7x +5) +C
Therefore the indefinite integral of sin (7x +5) is (-1/7) cos (7x +5) +C.
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