Solve (1-x)^4 (6 x ln x + x^3 - 6 x^2 + 3 x + 2)/6

Pergunta

Simplify the expression

\frac{6 x ln ( x ) - 24 x ^{2} ln ( x ) + 36 x ^{3} ln ( x ) - 24 x ^{4} ln ( x ) + 6 x ^{5} ln ( x ) + 35 x ^{3} - 50 x ^{4} + 33 x ^{5} - 10 x ^{6} + x ^{7} - 6 x ^{2} - 5 x + 2}{6}

Evaluate

(1 - x)^{4} \times \frac{6 x ln ( x ) + x ^{3} - 6 x ^{2} + 3 x + 2}{6}

Multiply the terms

\frac{( 1 - x ) ^{4} ( 6 x ln ( x ) + x ^{3} - 6 x ^{2} + 3 x + 2 )}{6}

Multiply the terms

Mais Passos

\frac{6 x ( 1 - x ) ^{4} \times ln ( x ) + x ^{3} ( 1 - x ) ^{4} - 6 x ^{2} ( 1 - x ) ^{4} + 3 x ( 1 - x ) ^{4} + 2 ( 1 - x ) ^{4}}{6}

Solução

Mais Passos

Evaluate

6 x (1 - x)^{4} \times ln (x) + x^{3} (1 - x)^{4} - 6 x^{2} (1 - x)^{4} + 3 x (1 - x)^{4} + 2 (1 - x)^{4}

Expand the expression

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + x^{3} (1 - x)^{4} - 6 x^{2} (1 - x)^{4} + 3 x (1 - x)^{4} + 2 (1 - x)^{4}

Expand the expression

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + x^{3} - 4 x^{4} + 6 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} (1 - x)^{4} + 3 x (1 - x)^{4} + 2 (1 - x)^{4}

Expand the expression

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + x^{3} - 4 x^{4} + 6 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} + 24 x^{3} - 36 x^{4} + 24 x^{5} - 6 x^{6} + 3 x (1 - x)^{4} + 2 (1 - x)^{4}

Expand the expression

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + x^{3} - 4 x^{4} + 6 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} + 24 x^{3} - 36 x^{4} + 24 x^{5} - 6 x^{6} + 3 x - 12 x^{2} + 18 x^{3} - 12 x^{4} + 3 x^{5} + 2 (1 - x)^{4}

Expand the expression

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + x^{3} - 4 x^{4} + 6 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} + 24 x^{3} - 36 x^{4} + 24 x^{5} - 6 x^{6} + 3 x - 12 x^{2} + 18 x^{3} - 12 x^{4} + 3 x^{5} + 2 - 8 x + 12 x^{2} - 8 x^{3} + 2 x^{4}

Calculate the sum or difference

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + 35 x^{3} - 4 x^{4} + 6 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} - 36 x^{4} + 24 x^{5} - 6 x^{6} + 3 x - 12 x^{2} - 12 x^{4} + 3 x^{5} + 2 - 8 x + 12 x^{2} + 2 x^{4}

Calculate the sum or difference

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + 35 x^{3} - 50 x^{4} + 6 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} + 24 x^{5} - 6 x^{6} + 3 x - 12 x^{2} + 3 x^{5} + 2 - 8 x + 12 x^{2}

Add the terms

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + 35 x^{3} - 50 x^{4} + 33 x^{5} - 4 x^{6} + x^{7} - 6 x^{2} - 6 x^{6} + 3 x - 12 x^{2} + 2 - 8 x + 12 x^{2}

Subtract the terms

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + 35 x^{3} - 50 x^{4} + 33 x^{5} - 10 x^{6} + x^{7} - 6 x^{2} + 3 x - 12 x^{2} + 2 - 8 x + 12 x^{2}

Calculate the sum or difference

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + 35 x^{3} - 50 x^{4} + 33 x^{5} - 10 x^{6} + x^{7} - 6 x^{2} + 3 x + 2 - 8 x

Subtract the terms

Mais Passos

6 x ln (x) - 24 x^{2} ln (x) + 36 x^{3} ln (x) - 24 x^{4} ln (x) + 6 x^{5} ln (x) + 35 x^{3} - 50 x^{4} + 33 x^{5} - 10 x^{6} + x^{7} - 6 x^{2} - 5 x + 2

\frac{6 x ln ( x ) - 24 x ^{2} ln ( x ) + 36 x ^{3} ln ( x ) - 24 x ^{4} ln ( x ) + 6 x ^{5} ln ( x ) + 35 x ^{3} - 50 x ^{4} + 33 x ^{5} - 10 x ^{6} + x ^{7} - 6 x ^{2} - 5 x + 2}{6}

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