Find the indefinite integral. 5x4 +7 dx (x5 +7x) Step 1 In this situation, finding the...

Transcribed Image Text:

Find the indefinite integral. 5x4 +7 dx (x5 +7x) Step 1 In this situation, finding the indefinite integral is most easily achieved using the method of integration by substitution. The first step in this method is to let u = g(x), where g(x) is part of the integrand and is usually the "inside function" of a composite function f(g(x)). 5x4 +7 (x5 +7x) For the given indefinite integral Therefore, we will choose u = x5+ 7x dx, observe that the integrand involves the composite function (x5+ 7x) with the "inside function" g(x) = x5 + 7x. 7x Step 2 The next step is to find du = g'(x) dx. First find g'(x). g(x) = x5 +7x g'(x) = Therefore, we have the following. du = dx Find the indefinite integral. 5x4 +7 dx (x5 +7x) Step 1 In this situation, finding the indefinite integral is most easily achieved using the method of integration by substitution. The first step in this method is to let u = g(x), where g(x) is part of the integrand and is usually the "inside function" of a composite function f(g(x)). 5x4 +7 (x5 +7x) For the given indefinite integral Therefore, we will choose u = x5+ 7x dx, observe that the integrand involves the composite function (x5+ 7x) with the "inside function" g(x) = x5 + 7x. 7x Step 2 The next step is to find du = g'(x) dx. First find g'(x). g(x) = x5 +7x g'(x) = Therefore, we have the following. du = dx