Find the indefinite integral ( x 3 x 1 x 1 x 2 ) dx Step 1 As the integral( x 3 x 1 x 1 x 2 ) dx has a sum as the integrand, we use the Sum Rule for Integration, ( f ( x ) g ( x )) dx f ( x ) dx g ( x ) dx , which says that we can break up integrals at sums and differences Our integral is thus ( x 3 x 1 x 1 x 2 ) dx x 3 dx x dx 1 dx x 1 dx x 2 2 dx Step 2 Now, we use the Power Rule for Integration from the text, x a dx 1 a 1 x a 1 C , on the first, second, and last integrals x 3 dx x dx 1 dx x 1 dx x 2 dx 1 1 2 x 1 dx x 1 dx x 1 C

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Find the indefinite integral  ( x 3   x   1   x 1   x 2 ) dx Step 1 As the integral( x 3   x   1   x 1   x 2 ) dx has a sum as the integrand, we use the Sum Rule for Integration, ( f ( x )   g ( x )) dx   f ( x ) dx   g ( x ) dx , which says that we can break up integrals at sums and differences  Our integral is thus ( x 3   x   1   x 1   x 2 ) dx   x 3 dx   x dx  1 dx   x 1 dx   x  2  2 dx   Step 2 Now, we use the Power Rule for Integration from the text, x a dx  1 a   1 x a   1   C , on the first, second, and last integrals  x 3 dx   x dx  1 dx   x 1 dx   x 2 dx  1  1 2 x  1 dx   x 1 dx   x 1   C

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Question: Find the indefinite integral. ( x 3 + x + 1 + x 1 + x 2 ) dx Step 1 As the integral( x

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