91Ó°ÊÓ

Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. $$\int \frac{y^{4}+y^{2}-1}{y^{3}+y} d y$$

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. $$\int \frac{1}{\sqrt{x^{2}+2 x+5}} d x$$ (Hint: Complete the square.)

Evaluate the integrals. Some integrals do not require integration by parts. $$\int x^{3} e^{x^{4}} d x$$

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$\int \frac{2 \theta^{3}-7 \theta^{2}+7 \theta}{2 \theta-5} d \theta$$

Evaluate the integrals. $$\int \sec ^{2} x \tan ^{2} x d x$$

Use an appropriate substitution and then a trigonometric substitution to evaluate the integrals. \(\int_{1}^{e} \frac{d y}{y \sqrt{1+(\ln y)^{2}}}\)

Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. $$\int \frac{d \theta}{\cos \theta-1}$$

Evaluate the integrals. $$\int \sec ^{4} x \tan ^{2} x d x$$

Use a substitution to change the integral into one you can find in the table. Then evaluate the integral. $$\int \frac{x^{2}}{\sqrt{x^{2}-4 x+5}} d x$$

Evaluate the integrals. Some integrals do not require integration by parts. $$\int x^{5} e^{x^{3}} d x$$