Solve ∫ (2^3+3^5)^2dt

$$\int ( 2 ^ { 3 } + 3 ^ { 5 } ) ^ { 2 } d t$$

Evaluate

$$63001t+С$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\int \left(8+3^{5}\right)^{2}\mathrm{d}t$$

Calculate 3 to the power of 5 and get 243.

$$\int \left(8+243\right)^{2}\mathrm{d}t$$

Add 8 and 243 to get 251.

$$\int 251^{2}\mathrm{d}t$$

Calculate 251 to the power of 2 and get 63001.

$$\int 63001\mathrm{d}t$$

Find the integral of 63001 using the table of common integrals rule \int a\mathrm{d}t=at.

$$63001t$$

If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$63001t+С$$

Differentiate w.r.t. t

$$63001$$