Evaluate the integral. {eq}\int 4x^2 \sqrt[4]{6+2x^3}dx {/eq} A. {eq}\frac{16}{5}(6+2x^3)^{5/4}+c {/eq} B. {eq}4(6+2x^3) ^{5/4}+c {/eq} C. {eq}- \frac{8}{3}(6+2x^3)^{-3/4}+...
Evaluate the integral of (x + 2)/(cube root of (e + x^2 + 4x)) dx. Evaluate the following integral and show all steps clearly \int_{2}^{\sqrt {5 \sqrt {x^2 - 4}/x^3 dx Evaluate the integral. integral_{0}^{1 / 6} \frac{11}{square ...
To evaluate the integral∫−15x√x+1dx, we will follow these steps: Step 1: Set up the integral We start with the given integral: I=∫1−15x4√x5+1dx Step 2: Use substitution Let us make the substitution: t=x5+1 Then, differentiate both sides with respect tox: ...
To evaluate the integral I=∫xcos2xdx, we will follow these steps: Step 1: Rewrite cos2x using a trigonometric identityWe know that:cos2x=1+cos2x2Thus, we can rewrite the integral as:I=∫xcos2xdx=∫x(1+cos2x2)dx=12∫x(1+cos2x)dx Step 2: Split the integralNow we can split ...
Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples. Related to this Question Evaluate the integral. integral dx/sqrt(x^2+16)
31K Explore the steps in integration by substitution. Learn the importance of integration with the chain rule and see the u-substitution formula with various examples. Related to this QuestionEvaluate the integral. (Use C for the constant of integration.) Evaluate the...
Evaluate the integral. ∫192ln(x)x2dx Step1 To use the integration-by-parts formula∫udv=uv-∫vdu, we must choose one part of∫192lnx)x2dxto beu,with the rest becoming dv. Chooseu=2ln(x).This means that...
Since 1414 is constant with respect to uu, move 1414 out of the integral. 9x+C−32272(13x3+C)+6(56x65+C)+12(14∫eudu)+∫−5xdx9x+C-32272(13x3+C)+6(56x65+C)+12(14∫eudu)+∫-5xdxSimplify. Tap for more steps... 9x+C−32272(x33+C)+6(5x656+C)+12(14∫eudu)...
Tap for more steps... ∫−1√udu∫-1udu Since−1-1isconstantwith respect touu, move−1-1out of theintegral. −∫√udu-∫udu Usen√ax=axnaxn=axnto rewrite√uuasu12u12. −∫u12du-u12 By thePower Rule, theintegralofu12u12with respect touuis23u3223u32. ...
Example Video Example (a) Evaluate the integral below as an infinite series. (b) Evaluate the integral below correct to within an error of 0.0001. 0.5 Solution (a) First we find the Maclaurin series for f(x) = ex. Although it's possible to ...