Final Answer
$\frac{t^{10}}{10}+\frac{15}{7}t^{7}+\frac{75}{4}t^{4}+125t+C_0$
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Step-by-step Solution
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1
Simplify the expression inside the integral
$\int\left(t^{3}+5\right)^3dt$
Learn how to solve integrals with radicals problems step by step online.
$\int\left(t^{3}+5\right)^3dt$
Learn how to solve integrals with radicals problems step by step online. Integrate int((tt^4^1/2+5)^3)dt. Simplify the expression inside the integral. Rewrite the integrand \left(t^{3}+5\right)^3 in expanded form. Expand the integral \int\left(t^{9}+15t^{6}+75t^{3}+125\right)dt into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int t^{9}dt results in: \frac{t^{10}}{10}.
Final Answer
$\frac{t^{10}}{10}+\frac{15}{7}t^{7}+\frac{75}{4}t^{4}+125t+C_0$