Calculus

Integration by Parts

Integration method for products

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Integration by parts steps:

1

Choose u and dv

u=x,  dv=ex dxu=x,\;dv=e^x\,dx
2

Find du and v

du=1 dx,  v=exdu=1\,dx,\;v=e^x
3

Apply the formula

∫x⋅ex dx=(x)(ex)−∫(ex)(1 dx)\int x\cdot e^x\,dx = (x)(e^x) - \int(e^x)(1\,dx)
4

Result

xex−ex+Cxe^x-e^x+C
∫u dv=uv−∫v du\int u\,dv = uv - \int v\,du

Integration by parts = reversing the product rule. LIATE rule for choosing u: Logarithmic, Inverse trig, Algebraic, Trig, Exponential.