Final answer to the problem
$\left(\frac{t^{11}}{11}+\frac{5}{9}t^{9}+\frac{10}{7}t^{7}+2t^{5}+\frac{5}{3}t^{3}+t\right)t-\frac{1}{2}t^2-\frac{5}{12}t^{4}-\frac{1}{3}t^{6}-\frac{5}{28}t^{8}-\frac{1}{18}t^{10}-\frac{1}{132}t^{12}+C_0$
Got another answer? Verify it here!
Step-by-step Solution
Specify the solving method
1
We can solve the integral $\int t\left(t^2+1\right)^5dt$ by applying integration by parts method to calculate the integral of the product of two functions, using the following formula
$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Learn how to solve differential calculus problems step by step online.
$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
Learn how to solve differential calculus problems step by step online. Find the integral int(t(t^2+1)^5)dt. We can solve the integral \int t\left(t^2+1\right)^5dt by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.
Final answer to the problem
$\left(\frac{t^{11}}{11}+\frac{5}{9}t^{9}+\frac{10}{7}t^{7}+2t^{5}+\frac{5}{3}t^{3}+t\right)t-\frac{1}{2}t^2-\frac{5}{12}t^{4}-\frac{1}{3}t^{6}-\frac{5}{28}t^{8}-\frac{1}{18}t^{10}-\frac{1}{132}t^{12}+C_0$