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Problem 47 Hard Difficulty

Evaluate the indefinite integral.

$ \displaystyle \int x(2x + 5)^8 \, dx $


$\frac{1}{40}(2 x+5)^{10}-\frac{5}{36}(2 x+5)^{9}+C$

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Video Transcript

Okay. The first thing we know is that we can make our you equivalent to two X plus five, which means our detox is 1/2. Do you remember? The derivative of five is simply zero. It's a constant. It doesn't moderate this context. Okay, Now this means we have the interval of humanness. Five over too times you to the eighth terms. 1/2 do you, which is simplified toe 1/4 times the integral of you to the ninth, minus five. You to the eighth D'You Using the power rule, we increased the exponents by wand. Then we divide by the new exponents. So you do. The ninth becomes you to the 10th divide by the new Explain it. Like I said. Now back. Substitute that you is to expose five. And don't forget your plus c