What is the integral of (2x+3)^{100} ?

The integral of (2x+3)^{100} is (2x+3)^{100}x-50(1/101 (2x+3)^{101}-3/100 (2x+3)^{100})+C

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integral of (2x+3)^{100}

\int (2 x + 3)^{100} d x

(2 x + 3)^{100} x - 50 (\frac{1}{101} (2 x + 3)^{101} - \frac{3}{100} (2 x + 3)^{100}) + C

Solution steps

\int (2 x + 3)^{100} d x

Apply Integration By Parts

: (2 x + 3)^{100} x - \int 200 (2 x + 3)^{99} x d x

= (2 x + 3)^{100} x - \int 200 (2 x + 3)^{99} x d x

\int 200 (2 x + 3)^{99} x d x = 50 (\frac{1}{101} (2 x + 3)^{101} - \frac{3}{100} (2 x + 3)^{100})

= (2 x + 3)^{100} x - 50 (\frac{1}{101} (2 x + 3)^{101} - \frac{3}{100} (2 x + 3)^{100})

Add a constant to the solution

= (2 x + 3)^{100} x - 50 (\frac{1}{101} (2 x + 3)^{101} - \frac{3}{100} (2 x + 3)^{100}) + C

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What is the integral of (2x+3)^{100} ?
The integral of (2x+3)^{100} is (2x+3)^{100}x-50(1/101 (2x+3)^{101}-3/100 (2x+3)^{100})+C