What is the integral from x to x^4 of y/x ?

The integral from x to x^4 of y/x is (x(x^6-1))/2

Popular >

integral from x to x^4 of y/x

\int_{x}^{x^{4}} \frac{y}{x} d y

\frac{x ( x ^{6} - 1 )}{2}

Solution steps

\int_{x}^{x^{4}} \frac{y}{x} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{x} \cdot \int_{x}^{x^{4}} y d y

Apply the Power Rule

: [\frac{y ^{2}}{2}]_{x}^{x^{4}}

= \frac{1}{x} [\frac{y ^{2}}{2}]_{x}^{x^{4}}

Simplify

\frac{1}{x} [\frac{y ^{2}}{2}]_{x}^{x^{4}} : \frac{[ \frac{y ^{2}}{2} ] _{x}^{x^{4}}}{x}

= \frac{[ \frac{y ^{2}}{2} ] _{x}^{x^{4}}}{x}

Compute the boundaries:

\frac{x ^{8}}{2} - \frac{x ^{2}}{2}

= \frac{\frac{x ^{8}}{2} - \frac{x ^{2}}{2}}{x}

Simplify

= \frac{x ( x ^{6} - 1 )}{2}

\int_{0}^{π} sin^{4} (x) cos (x) d x

\int_{0}^{1} e^{x + x^{2}} d x

\int_{- 1}^{0} (x - x^{2}) d x

\int_{1}^{2} x^{3} + 3 x d x

\int_{50}^{100} \frac{1}{x} d x

What is the integral from x to x^4 of y/x ?
The integral from x to x^4 of y/x is (x(x^6-1))/2