- #1
KDeep
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Homework Statement
∫xtan^-1(x^2)dx
Homework Equations
The Attempt at a Solution
I did u = x, du = 1,
v = ? ,dv = tan^-1(x^2)dx
I do not know how to get the integral of tan^-1(x^2)
KDeep said:Homework Statement
∫xtan^-1(x^2)dxHomework Equations
The Attempt at a Solution
I did u = x, du = 1dx,
v = ? ,dv = tan^-1(x^2)dx
I do not know how to get the integral of tan^-1(x^2)
LCKurtz said:u = x can never simplify an integral. It just changes the name of the variable. Try ##u=x^2##.
KDeep said:Correct?
LCKurtz said:Did you forget an arctangent?
KDeep said:u = x^2
du = 2xdx
du/2 = xdx
∫xtan^1(x^2)dx
(1/2)∫tan^-1(u)du
I cannot figure out the integral of tan^-1(u)
Trigonometric substitution is a method used in integral calculus to solve integrals that involve expressions containing trigonometric functions.
Trigonometric substitution is used when an integral cannot be solved using other techniques such as u-substitution or integration by parts. It is particularly useful for integrals involving radicals and expressions containing both quadratic and linear terms.
Trigonometric substitution involves substituting an expression in the integral with a trigonometric function and using trigonometric identities to simplify the integral. The chosen trigonometric function is typically one that will cancel out or simplify other terms in the integral.
Yes, there are three main types of trigonometric substitution: the substitution of sine and cosine, the substitution of tangent and secant, and the substitution of cotangent and cosecant. The type of substitution used depends on the form of the integral.
No, trigonometric substitution can only be used for certain types of integrals. It is important to recognize when it is appropriate to use trigonometric substitution and when other techniques should be used instead.