What is 1/(cos^3(x))dx ?

The solution to 1/(cos^3(x))dx is sec^3(x)dx

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simplify 1/(cos^3(x))dx

simplify

\frac{1}{cos ^{3} ( x )} d x

sec^{3} (x) d x

Solution steps

\frac{1}{cos ^{3} ( x )} d x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot d x}{cos ^{3} ( x )}

Multiply:

1 \cdot d x = d x

= \frac{d x}{cos ^{3} ( x )}

Use the basic trigonometric identity:

\frac{1}{cos ( x )} = sec (x)

= d x sec^{3} (x)

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