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أكمل
∫x3cosxdx\int_{ }^{ }x^3\cos xdx∫x3cosxdx =
tanx−c\tan x-ctanx−c
ln∣secx+tanx∣\ln\left|\sec x+\tan x\right|ln∣secx+tanx∣
x3sinx+3x2cosx−6xsinx−6cosx+cx^3\sin x+3x^2\cos x-6x\sin x-6\cos x+cx3sinx+3x2cosx−6xsinx−6cosx+c
:إملأ الفراغ
∫xlnxdx=........\int_{ }^{ }x\ln xdx=........∫xlnxdx=........
12x2(lnx−12)+c\frac{1}{2}x^2\left(\ln x-\frac{1}{2}\right)+c21x2(lnx−21)+c
xlnx−x+cx\ln x-x+cxlnx−x+c
∫sin−1xdx=\int_{ }^{ }\sin^{-1}xdx=∫sin−1xdx=
xsin−1x−1−x2+cx\sin^{-1}x-\sqrt{1-x^2}+cxsin−1x−1−x2+c
∫x3lnxdx=.......\int_{ }^{ }x^3\ln xdx=.......∫x3lnxdx=.......
x44(lnx−14)+c\frac{x^4}{4}\left(\ln x-\frac{1}{4}\right)+c4x4(lnx−41)+c
x33(lnx−13)+c\frac{x^3}{3}\left(\ln x-\frac{1}{3}\right)+c3x3(lnx−31)+c
∫x4lnxdx=..........\int_{ }^{ }x^4\ln xdx=..........∫x4lnxdx=..........
x55(lnx−15)+c\frac{x^5}{5}\left(\ln x-\frac{1}{5}\right)+c5x5(lnx−51)+c
∫xcosxdx=.......\int_{ }^{ }x\cos xdx=.......∫xcosxdx=.......
xsinx+cosx+cx\sin x+\cos x+cxsinx+cosx+c
sinx−xcosx+c\sin x-x\cos x+csinx−xcosx+c
∫x2lnxdx=.......\int_{ }^{ }x^2\ln xdx=.......∫x2lnxdx=.......
12x2(lnx−12)\frac{1}{2}x^2\left(\ln x-\frac{1}{2}\right)21x2(lnx−21)
∫e−x(cosx−sinx)dx=\int_{ }^{ }e^{-x}\left(\cos x-\sin x\right)dx=∫e−x(cosx−sinx)dx=
x44(e−xsinx+c−14)+c\frac{x^4}{4}\left(e^{-x}\sin x+c-\frac{1}{4}\right)+c4x4(e−xsinx+c−41)+c
e−xsinx+ce^{-x}\sin x+ce−xsinx+c
x33(e−xsinx+c−13)+c\frac{x^3}{3}\left(e^{-x}\sin x+c-\frac{1}{3}\right)+c3x3(e−xsinx+c−31)+c
∫t2.lntdt =\int_{ }^{ }t^2.\ln tdt\ =∫t2.lntdt =
12t2(lnt−12)+c\frac{1}{2}t^2\left(\ln t-\frac{1}{2}\right)+c21t2(lnt−21)+c
tlnt−t+ct\ln t-t+ctlnt−t+c
t33(lnt−13)+c\frac{t^3}{3}\left(\ln t-\frac{1}{3}\right)+c3t3(lnt−31)+c
∫x(Tan−1x)dx\int_{ }^{ }x\left(Tan^{-1}x\right)dx∫x(Tan−1x)dx =
tanx-c
12tanx−1(x2+1)−12x+c\frac{1}{2}\tan x^{-1}\left(x^2+1\right)-\frac{1}{2}x+c21tanx−1(x2+1)−21x+c
sinx−cosx+c\sin x-\cos x+csinx−cosx+c
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