# Power series Calculator

## Get detailed solutions to your math problems with our Power series step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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### Difficult Problems

1

Solved example of power series

$\int\sin\left(4x\right)\cdot\cos\left(2x\right)dx$
2

Apply the formula: $\sin\left(x\right)\cos\left(y\right)$$=\frac{\sin\left(x+y\right)+\sin\left(x-y\right)}{2}, where x=4x and y=2x \int\frac{\sin\left(4x+2x\right)+\sin\left(4x-2x\right)}{2}dx Adding 4x and 2x \int\frac{\sin\left(6x\right)+\sin\left(4x-2x\right)}{2}dx Adding 4x and -2x \int\frac{\sin\left(6x\right)+\sin\left(2x\right)}{2}dx 3 Simplifying \int\frac{\sin\left(6x\right)+\sin\left(2x\right)}{2}dx 4 Split the fraction \frac{\sin\left(6x\right)+\sin\left(2x\right)}{2} inside the integral, in two terms with common denominator 2 \int\left(\frac{\sin\left(6x\right)}{2}+\frac{\sin\left(2x\right)}{2}\right)dx 5 The integral of the sum of two or more functions is equal to the sum of their integrals \int\frac{\sin\left(6x\right)}{2}dx+\int\frac{\sin\left(2x\right)}{2}dx Take the constant out of the integral \frac{1}{2}\int\sin\left(6x\right)dx Apply the formula: \int\sin\left(ax\right)dx$$=-\left(\frac{1}{a}\right)\cos\left(ax\right)$, where $a=6$

$-\frac{1}{12}\cos\left(6x\right)$
6

The integral $\int\frac{\sin\left(6x\right)}{2}dx$ results in: $-\frac{1}{12}\cos\left(6x\right)$

$-\frac{1}{12}\cos\left(6x\right)$

Take the constant out of the integral

$\frac{1}{2}\int\sin\left(2x\right)dx$

Apply the formula: $\int\sin\left(ax\right)dx$$=-\left(\frac{1}{a}\right)\cos\left(ax\right)$, where $a=2$

$-\frac{1}{4}\cos\left(2x\right)$
7

The integral $\int\frac{\sin\left(2x\right)}{2}dx$ results in: $-\frac{1}{4}\cos\left(2x\right)$

$-\frac{1}{4}\cos\left(2x\right)$
8

Gather the results of all integrals

$-\frac{1}{12}\cos\left(6x\right)-\frac{1}{4}\cos\left(2x\right)$
9

As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration

$-\frac{1}{12}\cos\left(6x\right)-\frac{1}{4}\cos\left(2x\right)+C_0$

$-\frac{1}{12}\cos\left(6x\right)-\frac{1}{4}\cos\left(2x\right)+C_0$