Nettet2 ∫ 0 π / 2 tan x d x but now, evaluating this integral is giving me some problems, simply substituting u = tan ( x) and then d u = sec 2 ( x) d x ⇒ d u 1 + u 2 = d x and which in turn gives something a bit ugly, I was wondering which is the most elegant way to evaluate this? calculus integration trigonometry definite-integrals Share Cite Follow NettetFind the indefinite integral. (Use \( C \) for the constant of integration.) \[ \int \sqrt[5]{\tan (7 x)} \sec ^{2}(7 x) d x \] -11 Points] Find an equation for the function \( f \) that has the given derivative and whose graph passes through the given point.
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Nettet18. mar. 2024 · Explanation: We begin with a u-substitution with u = √tanx The derivative of u is: du dx = sec2(x) 2√tanx so we divide by that to integrate with respect to u (and remember, dividing by a fraction is the same as multiplying by its reciprocal): ∫ 1 √tanx dx = ∫ 1 √tanx ⋅ 2√tanx sec2x du = = ∫ 2 sec2x du Nettet24. nov. 2016 · You can also see this this way: ∫sec2xtanxdx = ∫secx(secxtanx)dx. If u = secx then du = secxtanxdx so. = ∫udu = u2 2 = sec2x 2 +C. This is equivalent to the other answer of tan2x 2 +C because tan2x and sec2x are only a constant away from one another through the equality tan2x + 1 = sec2x. Answer link. first instance of condoms
Integral sqrt(tanx) Integration sqrt(tanx) - YouTube
Nettet15. feb. 2024 · This intimidating integration of square root of tanx can be solved by distinct techniques. The first method I will describe is the most elegant, but requires … Nettet16. mai 2024 · Statement I The value of the integral ∫(x → pi/3,pi/6)dx/(1 + √tanx) is equal to pi/6. asked Oct 11, 2024 in Mathematics by Samantha (39.3k ... Prove that ∫f(x) dx, x ∈ [2, b] = ∫f(a + b - x)dx, x ∈ [a, b] and hence evaluate ∫dx/1 + √tanx, x ∈ [π/3, π/3] asked Jan 26, 2024 in Mathematics by Pankaj01 (50.7k ... NettetMath; Calculus; Calculus questions and answers; Find the indefinite integral. (Use \( C \) for the constant of integration.) \[ \int \sqrt[5]{\tan (7 x)} \sec ^{2}(7 x) d x \] -11 Points] … first instance of human flight