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Popular >

integral of x^7sin(x^8)

Solution

\int x^{7} sin (x^{8}) d x

Solution

- \frac{1}{8} cos (x^{8}) + C

Solution steps

\int x^{7} sin (x^{8}) d x

Apply u-substitution

: \int \frac{sin ( u )}{8} d u

= \int \frac{sin ( u )}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= \frac{1}{8} (- cos (u))

Substitute back

u = x^{8}

= \frac{1}{8} (- cos (x^{8}))

Simplify

= - \frac{1}{8} cos (x^{8})

Add a constant to the solution

= - \frac{1}{8} cos (x^{8}) + C

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\frac{d}{d x} (e^{x^{2}} + 1)

tangent of y=2x^2 tangent of

y = 2 x^{2}

integral from 0 to y+z of 1/((x+y+z)^3)

\int_{0}^{y + z} \frac{1}{( x + y + z ) ^{3}} d x

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e^{x} (x - 1)

y^'+sin(t)y=sin(t),y(0)=6

y^{^{'}} + sin (t) y = sin (t), y (0) = 6

Frequently Asked Questions (FAQ)

What is the integral of x^7sin(x^8) ?
The integral of x^7sin(x^8) is -1/8 cos(x^8)+C