13.08 Integration using substitution
Consider the integral \int 5 \left( 5 x + 4\right)^{3} dx and the substitution u = 5 x + 4.
Find \dfrac{d u}{d x}.
Hence, find \int 5 \left( 5 x + 4\right)^{3} dx.
Find \int 2 x \left(x^{2} - 5\right)^{7} dx using the substitution u = x^{2} - 5.
Find \int 3 x^{2} \left(x^{3} + 7\right)^{4} dx using the substitution u = x^{3} + 7.
Find \int \dfrac{6 x}{\left( 3 x^{2} + 2\right)^{2}} dx using substitution.
Consider the definite integral \int_{0}^{2} 3 \left( 3 x - 6\right)^{2} dx and the substitution u = 3 x - 6.
Find the value of u when the value of x is:
Find \dfrac{d u}{d x}.
What does the integral, \int_{0}^{2} 3 \left( 3 x - 6\right)^{2} dx, become after making the substitution \\ u = 3 x - 6?
Evaluate this integral.
Find \int_{0}^{3} 9 \left(x + 3\right)^{2} dx using the substitution u = x + 3.
Find \int_{6}^{8} \left( 3 x - 15\right)^{2} dx using the substitution u = 3 x - 15.
Find \int_{1}^{2} 4 x \left( 2 x^{2} - 2\right)^{2} dx using the substitution u = 2 x^{2} - 2.
Find \int_{ - 1 }^{2} 64 x \left( 4 x^{2} + 1\right)^{3} dx using the substitution u = 4 x^{2} + 1.
Find \int_{0}^{1} \dfrac{- 144 x^{3}}{\left( 2 x^{4} - 3\right)^{3}} dx using the substitution u = 2 x^{4} - 3.
Find \int_{ - 2 }^{1} \dfrac{24}{\left(\dfrac{x + 5}{3}\right)^{4}} dx using the substitution u = \dfrac{x + 5}{3}.
Find the following definite integrals using substitution: