1)
∫x3(x4+16)3dx u=x4+16,du=4x3dx,x3dx=41du
∫x3(x4+16)3dx=41∫u3du=161u4+C
=161(x4+16)4+C
2)
∫3x2(x3+5)7dx u=x3+5,du=3x2dx
∫3x2(x3+5)7dx=∫u7du=81u8+C
=81(x3+5)8+C
3)
∫1−x4x3dx u=1−x4,du=−4x3dx,x3dx=−41du
∫1−x4x3dx=−41∫udu=−21u+C
=−211−x4+C
4)
∫(cosx)3sinxdx u=cosx,du=−sinxdx
∫(cosx)3sinxdx=−∫u31du=2u21+C
=2(cosx)21+C
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