QQuestionMathematics
QuestionMathematics
"Find the following indefinite integral:
integral square root of x left parenthesis 5 x plus 3 right parenthesis squared d x
a. 50 over 7 x to the power of 7 over 2 end exponent plus 12 x to the power of 5 over 2 end exponent plus 6 x to the power of 3 over 2 end exponent plus c
b. 50 over 7 x to the power of 7 over 2 end exponent plus 6 x to the power of 3 over 2 end exponent plus c
c. 175 over 2 x to the power of 7 over 2 end exponent plus 75 x to the power of 5 over 2 end exponent plus 27 over 2 x to the power of 3 over 2 end exponent plus c
d. 175 over 2 x to the power of 7 over 2 end exponent plus 27 over 2 x to the power of 3 over 2 end exponent plus c"
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Answer
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Step 1: Identify the function we need to integrate.
\int \sqrt{x}(5x+3)^2 dx
Step 2: We can simplify the integrand by expanding $(5x+ 3)^1$ and then taking the square root of $x$ outside the parentheses.
\int (25x^2+30x+9) \sqrt{x} dx
Final Answer
\boxed{\frac{50}{7}x^{7 / 2} + \frac{12}{5}x^{5 / 2} + 6x^{3 / 2} + C}
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