Solve ∫ (from 0 to 1) of t^2d(arctant)

$$\int _ { 0 } ^ { 1 } t ^ { 2 } d ( \arctan t )$$

Evaluate

$$dt^{2}\arctan(t)$$

Solution Steps

Evaluate the indefinite integral first.

$$\int t^{2}d\arctan(t)\mathrm{d}x$$

Find the integral of t^{2}d\arctan(t) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$t^{2}d\arctan(t)x$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$t^{2}d\arctan(t)+0t^{2}d\arctan(t)$$

Simplify.

$$t^{2}d\arctan(t)$$

Differentiate w.r.t. t

$$\frac{dt\left(2t^{2}\arctan(t)+2\arctan(t)+t\right)}{t^{2}+1}$$