What is the integral of (x+1)sqrt(8x+9) ?

The integral of (x+1)sqrt(8x+9) is 1/12 (x+1)(8x+9)^{3/2}-1/240 (8x+9)^{5/2}+C

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integral of (x+1)sqrt(8x+9)

\int (x + 1) 8 x + 9 d x

\frac{1}{12} (x + 1) (8 x + 9)^{\frac{3}{2}} - \frac{1}{240} (8 x + 9)^{\frac{5}{2}} + C

Solution steps

\int (x + 1) 8 x + 9 d x

Apply Integration By Parts

: \frac{1}{12} (x + 1) (8 x + 9)^{\frac{3}{2}} - \int \frac{1}{12} (8 x + 9)^{\frac{3}{2}} d x

= \frac{1}{12} (x + 1) (8 x + 9)^{\frac{3}{2}} - \int \frac{1}{12} (8 x + 9)^{\frac{3}{2}} d x

\int \frac{1}{12} (8 x + 9)^{\frac{3}{2}} d x = \frac{1}{240} (8 x + 9)^{\frac{5}{2}}

= \frac{1}{12} (x + 1) (8 x + 9)^{\frac{3}{2}} - \frac{1}{240} (8 x + 9)^{\frac{5}{2}}

Add a constant to the solution

= \frac{1}{12} (x + 1) (8 x + 9)^{\frac{3}{2}} - \frac{1}{240} (8 x + 9)^{\frac{5}{2}} + C

\frac{2 x}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (x^{3} + 5 x + 7)

e^{- t} + 2 e^{- 2 t} + t e^{- 3 t}

\int \frac{5 cosh ( x )}{x} d x

n = 0 \sum \infty \frac{n}{2 n ^{2} + 1}

What is the integral of (x+1)sqrt(8x+9) ?
The integral of (x+1)sqrt(8x+9) is 1/12 (x+1)(8x+9)^{3/2}-1/240 (8x+9)^{5/2}+C