### Home > CALC > Chapter 6 > Lesson 6.3.2 > Problem6-91

6-91.

Examine the integrals below. Consider the multiple tools available for evaluating integrals and use the best strategy for each. After evaluating the integral, write a short description of your method.

1. $\int _ { 1 } ^ { 10 } 2 \sqrt { x - 1 } d x$

Convert the radical to an exponent. Then use the form upowerdu.

1. $\int ( 3 x - 2 ) ^ { 2 } d x$

Use the form for one of the inverse trig. functions.

1. $\int - \frac { 1 } { 1 + x ^ { 2 } } d x$

If $u = (3x − 2)$, then you need to add a $du$. In this case, it would be $3$ $dx$.  Since you already have a $dx$, add a $3$ taking out a $\left(1/3\right)$ to compensate.

Multiply $(3x − 2) (3x − 2)$.
Then take the antiderivative.

1. $\int ( 6 t ^ { - 3 / 2 } + 7 t ^ { 1 / 4 } ) d t$

Take the antiderivative.