tan(x) + C
d/dx tan(x) = d/dx (sin(x))/(cos(x)) = (sin^2(x)+cos^2(x))/(cos^2(x)) = 1/(cos^2(x)) = sec^2(x)
NEVER FORGET THE CONSTANT!
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integral of radical sinx
Note that for sec²(x) - tan²(x) = 1, we have: -tan²(x) = 1 - sec²(x) tan²(x) = sec²(x) - 1 Rewrite the expression as: ∫ (sec²(x) - 1) dx = ∫ sec²(x) dx - ∫ 1 dx Finally, integrate each expression to get: tan(x) - x + K where K is the arbitrary constant
The integral of sec(x) with respect to x is ln|sec(x) + tan(x)| + C, where C is the constant of integration. This result can be derived using integration techniques such as substitution or integration by parts. The integral of sec(x) is a common integral in calculus and is often used in trigonometric integrals.
The indefinite integral of (1/x^2)*dx is -1/x+C.
ln(sinx) + 1/3ln(sin3x) + C