∫20x(5x2+x-2) dx
∫4(102x^2) dx
∫(100x3+20x2−40x)dx=25x4+20x3/3−20x3+C\int(100x^3+20x^2-40x)dx=25x^4+20x^3/3-20x^3+C∫(100x3+20x2−40x)dx=25x4+20x3/3−20x3+C
4∫102x2dx4\smallint10^{2x^2}dx4∫102x2dx
u=2xu=\sqrt{2}xu=2x
du=2dxdu=\sqrt2dxdu=2dx
4∫102x2dx=42∫10u2du=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}du4∫102x2dx=24∫10u2du=423/2ln(10)π∫π2ln(10)10u2du
∫2ln(10)10u2πdu=erfi(ln(10)u)\intop\frac{2\sqrt{ln(10)}10^{u^2}}{\sqrtπ}du=erfi(\sqrt{ln(10)}u)∫π2ln(10)10u2du=erfi(ln(10)u)
4∫102x2dx=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)+C4∫102x2dx=423/2ln(10)πerfi(ln(10)u)=423/2ln(10)πerfi(ln(10)2x)+C
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