Integral of sec2(x)\sec^{2}{\left(x \right)}

The calculator will find the integral/antiderivative of sec2(x)\sec^{2}{\left(x \right)}, with steps shown.

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Your Input

Find sec2(x)dx\int \sec^{2}{\left(x \right)}\, dx.

Solution

The integral of sec2(x)\sec^{2}{\left(x \right)} is sec2(x)dx=tan(x)\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}:

sec2(x)dx=tan(x){\color{red}{\int{\sec^{2}{\left(x \right)} d x}}} = {\color{red}{\tan{\left(x \right)}}}

Therefore,

sec2(x)dx=tan(x)\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}

Add the constant of integration:

sec2(x)dx=tan(x)+C\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}+C

Answer: sec2(x)dx=tan(x)+C\int{\sec^{2}{\left(x \right)} d x}=\tan{\left(x \right)}+C