What is the integral of xcsc(tan(x^2))sec^2(x^2) ?

The integral of xcsc(tan(x^2))sec^2(x^2) is 1/2 ln|tan((tan(x^2))/2)|+C

Popular >

integral of xcsc(tan(x^2))sec^2(x^2)

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

\frac{1}{2} ln tan (\frac{tan ( x ^{2} )}{2}) + C

Solution steps

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

Apply u-substitution

: \int \frac{csc ( u )}{2} d u

= \int \frac{csc ( u )}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int csc (u) d u

Apply u-substitution

: \int \frac{1}{v} d v

= \frac{1}{2} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{2} ln ∣ v ∣

Substitute back

= \frac{1}{2} ln tan (\frac{tan ( x ^{2} )}{2})

Add a constant to the solution

= \frac{1}{2} ln tan (\frac{tan ( x ^{2} )}{2}) + C

\frac{\partial}{\partial x} (x^{4} + 5 x y^{3})

\int \frac{x ^{2}}{x ^{2} + x + 30} d x

f (x) = 2 x + 3, at x = 3

\int_{0}^{π} 3 x^{2} + cos (x) d x

\frac{x}{x ^{- 1} + 12}

What is the integral of xcsc(tan(x^2))sec^2(x^2) ?
The integral of xcsc(tan(x^2))sec^2(x^2) is 1/2 ln|tan((tan(x^2))/2)|+C