Solve \int (sec(x)tan(x))/( sqrt(sec(x))) dx - ScanMath

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Type your math problem... \int (sec(x)tan(x))/( sqrt(sec(x))) dx

Question

Evaluate the integral

2 sec (x) + C, C \in R

Evaluate

\int \frac{sec ( x ) tan ( x )}{sec ( x )} d x

Reduce the fraction

More Steps

\int sec^{\frac{1}{2}} (x) tan (x) d x

Rewrite the expression

\int cos^{- \frac{3}{2}} (x) sin (x) d x

Rewrite the expression

\int \frac{sin ( x )}{cos ^{\frac{3}{2}} ( x )} d x

Use the substitution d x = - \frac{1}{sin ( x )} d t to transform the integral

More Steps

\int \frac{sin ( x )}{cos ^{\frac{3}{2}} ( x )} \times (- \frac{1}{sin ( x )}) d t

Simplify

More Steps

\int - \frac{1}{cos ^{\frac{3}{2}} ( x )} d t

Use the substitution t = cos (x) to transform the integral

\int \frac{- 1}{t ^{\frac{3}{2}}} d t

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\int - \frac{1}{t ^{\frac{3}{2}}} d t

Use the property of integral \int k f (x) d x = k \int f (x) d x

- \int \frac{1}{t ^{\frac{3}{2}}} d t

Use the property of integral \int x^{n} d x = \frac{x ^{n + 1}}{n + 1}

- \frac{t ^{- \frac{3}{2} + 1}}{- \frac{3}{2} + 1}

Simplify

More Steps

- (- 2 t^{- \frac{1}{2}})

Calculate

2 t^{- \frac{1}{2}}

Substitute back

2 cos^{- \frac{1}{2}} (x)

Simplify

2 sec^{\frac{1}{2}} (x)

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

2 sec (x)

Solution

2 sec (x) + C, C \in R

Show Solution