Integral of udu
NettetThe Integral Calculator supports definite and indefinite integrals (antiderivatives) as well as integrating functions with many variables. You can also check your answers! … NettetThe function can be found by finding the indefinite integral of the derivative. Step 3. Set up the integral to solve. Step 4. Since is constant with respect to , move out of the …
Integral of udu
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Nettet∫ d u ( a 2 + u 2) 3 / 2 = ∫ a sec 2 x d x ( a 2 + a 2 tan 2 x) 3 / 2. Applying the trigonometric identity considered above, this becomes ∫ a sec 2 x d x ( a 2 sec 2 x) 3 / 2 = ∫ d x a 2 sec x = 1 a 2 ∫ cos x d x, which can be easily integrated as = 1 a 2 sin x. NettetNow, in order to rewrite dx dx in terms of du du, we need to find the derivative of u u. We need to calculate du du, we can do that by deriving the equation above u Applying the power rule for integration, ∫ x dx x n 1 8 u u x^2-3 x2 −3 2 C 0 Final Answer \frac {1} {4}\left (x^2-3\right)^2+C_0 41 (x2 3)2 +C 0
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http://www.math.com/tables/integrals/more/ln.htm Nettet1. Proof Strategy: Use Integration by Parts. ln (x) dx set u = ln (x), dv = dx then we find du = (1/x) dx, v = x substitute ln (x) dx = u dv and use integration by parts = uv - v du substitute u=ln (x), v=x, and du= (1/x)dx = ln (x) x - x (1/x) dx = ln (x) x - dx = ln (x) x - x + C = x ln (x) - x + C. Q.E.D.
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