Evaluate the integral. int(x^(2)+5)^(2)dx Answer:

Expand the integrand: We need to expand the integrand (x^2 + 5)^2 before integrating. (x^2 + 5)^2 = (x^2 + 5)(x^2 + 5) = x^4 + 10x^2 + 25Integrate the expanded form: Now we integrate the expanded form term by term. ∫(x^4 + 10x^2 + 25)dx = ∫x^4dx + ∫10x^2dx + ∫25dxIntegrate each term separately: Integrate each term separately using the power rule for integration, which states that ∫x^n dx = (x^(n+1))/(n+1) + C for any real number n ≠ -1. ∫x^4dx = (x^(4+1))/(4+1) = (x^5)/5 ∫10x^2dx = 10 * (x^(2+1))/(2+1) = (10x^3)/3 ∫25dx = 25xCombine the integration results: Combine the results of the integrations to get the final indefinite integral. ∫(x^4 + 10x^2 + 25)dx = (x^5)/5 + (10x^3)/3 + 25x + C

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Evaluate the integral.

int(x^(2)+5)^(2)dx
Answer:

Evaluate the integral. $\newline$ $\int\left(x^{2}+5\right)^{2} \mathrm{~d} x$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

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Q. Evaluate the integral.

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\int\left(x^{2}+5\right)^{2} \mathrm{~d} x

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Answer:

Expand the integrand: We need to expand the integrand $(x^2 + 5)^2$ before integrating. $(x^2 + 5)^2 = (x^2 + 5)(x^2 + 5) = x^4 + 10x^2 + 25$
Integrate the expanded form: Now we integrate the expanded form term by term. $\newline$ $\int(x^4 + 10x^2 + 25)\,dx = \int x^4\,dx + \int 10x^2\,dx + \int 25\,dx$
Integrate each term separately: Integrate each term separately using the power rule for integration, which states that $\int x^n \, dx = \frac{x^{(n+1)}}{(n+1)} + C$ for any real number $n \neq -1$ . $\int x^4\,dx = \frac{x^{(4+1)}}{(4+1)} = \frac{x^5}{5}$ $\int 10x^2\,dx = 10 \times \frac{x^{(2+1)}}{(2+1)} = \frac{10x^3}{3}$ $\int 25\,dx = 25x$
Combine the integration results: Combine the results of the integrations to get the final indefinite integral. $\newline$ $\int(x^4 + 10x^2 + 25)\,dx = \frac{x^5}{5} + \frac{10x^3}{3} + 25x + C$