# Find the indefinite integral by substitution. {eq}a) \int x^3(x^4 + 3)^2 dx \\ b) \int 3x^2 \sin x^3 dx {/eq}

## Question:

Find the indefinite integral by substitution.

{eq}a) \int x^3(x^4 + 3)^2 dx \\ b) \int 3x^2 \sin x^3 dx {/eq}

## Indefinite Integral :

The indefinite integral of a function given in the form {eq}\int f(x)\ f'(x) \ dx {/eq} can be evaluated by using the substitution method. Since, the function and its derivative both are given as a single function

therefore, if we take {eq}f(x)=t {/eq} then we will get {eq}f'(x)\ dx = dt {/eq} and hence the integral becomes easy to solve.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer!

a) Let the given integral be {eq}I {/eq} then we have:

{eq}I = \int x^{3}(x^{4} + 3)^{2} \ dx {/eq}

Take {eq}x^{4} + 3= t {/eq} so that we get...

See full answer below.