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Popular >

integral of cos^{17}(x)sin(x)

Solution

\int cos^{17} (x) sin (x) d x

Solution

- \frac{cos ^{18} ( x )}{18} + C

Solution steps

\int cos^{17} (x) sin (x) d x

Apply u-substitution

: \int - u^{17} d u

= \int - u^{17} d u

Take the constant out:

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

= - \int u^{17} d u

Apply the Power Rule

: \frac{u ^{18}}{18}

= - \frac{u ^{18}}{18}

Substitute back

u = cos (x)

= - \frac{cos ^{18} ( x )}{18}

Add a constant to the solution

= - \frac{cos ^{18} ( x )}{18} + C

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\int (9 x^{2} - 4 x + 3) d x

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

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\int x (x + 4)^{4} d x

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\int x csc (3 x^{2}) d x

integral of (cos(x-1))/(sin^2(x-1))

\int \frac{cos ( x - 1 )}{sin ^{2} ( x - 1 )} d x

Frequently Asked Questions (FAQ)

What is the integral of cos^{17}(x)sin(x) ?
The integral of cos^{17}(x)sin(x) is -(cos^{18}(x))/(18)+C