What is the integral of (x+1)^{10}(x+2) ?

The integral of (x+1)^{10}(x+2) is 1/11 (x+1)^{11}(x+2)-1/132 (x+1)^{12}+C

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integral of (x+1)^{10}(x+2)

\int (x + 1)^{10} (x + 2) d x

\frac{1}{11} (x + 1)^{11} (x + 2) - \frac{1}{132} (x + 1)^{12} + C

Solution steps

\int (x + 1)^{10} (x + 2) d x

Apply Integration By Parts

= \frac{1}{11} (x + 1)^{11} (x + 2) - \int \frac{1}{11} (x + 1)^{11} d x

\int \frac{1}{11} (x + 1)^{11} d x = \frac{1}{132} (x + 1)^{12}

= \frac{1}{11} (x + 1)^{11} (x + 2) - \frac{1}{132} (x + 1)^{12}

Add a constant to the solution

= \frac{1}{11} (x + 1)^{11} (x + 2) - \frac{1}{132} (x + 1)^{12} + C

d er i v a t i v e y = ln (sec (x))

x \to 0 lim ((\frac{1}{x})^{x^{2}})

\frac{d}{d x} (e^{- 2 x} (a cos (x) + b sin (x)))

x \to 0 + lim (\frac{6}{sin ( x )})

\frac{d y}{d x} + x y = y

What is the integral of (x+1)^{10}(x+2) ?
The integral of (x+1)^{10}(x+2) is 1/11 (x+1)^{11}(x+2)-1/132 (x+1)^{12}+C