Question #180974

∫20x(5x2+x-2) dx

∫4(102x^2) dx


1
Expert's answer
2021-04-26T08:16:57-0400

(100x3+20x240x)dx=25x4+20x3/320x3+C\int(100x^3+20x^2-40x)dx=25x^4+20x^3/3-20x^3+C


4102x2dx4\smallint10^{2x^2}dx

u=2xu=\sqrt{2}x

du=2dxdu=\sqrt2dx

4102x2dx=4210u2du=4π23/2ln(10)2ln(10)10u2πdu4\smallint10^{2x^2}dx=\frac{4}{\sqrt2}\smallint10^{u^2}du=4\frac{\sqrt{π}}{ 2^{3/2}\sqrt{ln(10)}}\intop\frac{2\sqrt{ln(10)}10^{u^2}}{\sqrtπ}du

2ln(10)10u2πdu=erfi(ln(10)u)\intop\frac{2\sqrt{ln(10)}10^{u^2}}{\sqrtπ}du=erfi(\sqrt{ln(10)}u)

4102x2dx=4π23/2ln(10)erfi(ln(10)u)=4π23/2ln(10)erfi(ln(10)2x)+C4\smallint10^{2x^2}dx=4\frac{\sqrt{π}}{ 2^{3/2}\sqrt{ln(10)}}erfi(\sqrt{ln(10)}u)=4\frac{\sqrt{π}}{ 2^{3/2}\sqrt{ln(10)}}erfi(\sqrt{ln(10)}\sqrt2x)+C





Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS