# U-substitution | Exercises

Here are some indefinite integrals you can practice with using u-sub. If you can’t solve all of them, don’t discourage. You can see the procedure for each here: https://addjustabitofpi.com/category/solutions/. This will help you understand the logics of integrals and you will eventually get the hang of it and be able to solve them right away! If you don’t remember the rules and properties of integrals, click this link: https://addjustabitofpi.com/rules-and-properties-of-integrals/.

$\int&space;x^2\cos(x^3-7)dx$ $\int&space;5kx^4e^{x^5}dx$ $\int&space;x\tan(3x^2)dx$ $\int&space;\sin(x+3)dx$ $\int&space;3e^{-3x+9}dx$ $\int&space;\cot(\varphi)d\varphi$

Notice that cot (cotangent) is the reciprocal of tan (tangent), which means that cot(x)=cos(x)/sin(x).

$\int&space;\sin(\frac{\pi^2}{6}\varphi)\sec(\frac{\pi^2}{6}\varphi)d\varphi$

Remember that sec (secant) is the reciprocal of cos (cosine), meaning that sec(x)=1/cos(x).

$\int&space;\cos(\pi&space;x)\csc(\pi&space;x)dx$

csc (cosecant) is the reciprocal of sin (sine), so csc(x)=1/sin(x).

$\int&space;\frac{\sec^2(x)}{\csc(x)}dx$

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